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Interview with Alexander Z. Patashinski,
part III
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PoS
General question. Do you have
any notes from some of the work that you did at that time?
Patashinski
Nothing that was not
published. There were local publications
that may be, I hope, found in the Lenin Library, because it was mandatory to
send a copy there, and I had some unpublished manuscripts, but I do not
have anything of that stuff here, in the US. My departure from the USSR was
not a normal and planned step. I was only allowed, in 1991, to go to Germany for a
service trip. I had to return
to Russia. Instead, I went
from Germany to US in 1992. At
that time, I was studying the structure of liquids and glasses, and I had
no notes on phase transitions with me.
PoS
You still maintain an office in
Novosibirsk?
Patashinski
Not any more. I submitted my resignation, for
family reasons, in 1997 or 1998, and this resignation was accepted. I
miss my Institute of Nuclear Physics, probably the best scientific
Institution I have known; that's, maybe, the only thing I really miss.
PoS
Do you have a copy of the
doctor of science [dissertation]?
Patashinski
Not here in the US. A copy of the
thesis was sent to the Lenin library in Moscow, and the dissertation was,
in somewhat modified form, published as part of a book, edited by Peter A.
Strelkov, published about 1968. I came to the US from Germany. I had the option of staying in Germany, and my idea was to commute between Russia and Germany.
PoS
That would be interesting.
Patashinski
My daughter Tanya moved to the US
with my half-year old grandson David, and they needed my help. I came here
first in 1991 and brought my wife Nadya to take care of the baby while my daughter
studies medicine. This was a difficult time for all us. Part of these
difficulties was that, until Gorbachev changed the Soviet system, I was
never permitted to go abroad, even when I was invited, about 1972, to take part in a Nobel Symposium. I had many wrong ideas about life in the West, and I had not fostered any ties and possible positions
that could help me find a place here, and I had very little command of
English.
PoS
This doctor of science thesis,
something that's not formally published, it would be very nice to add to
the archive.
Patashinski
One copy, I hope, is still in
my apartment in Novosibirsk. Here, I have the diplomas, Candidate and
Doctor of Science, and Professor of Physics and Math, etc., and the Landau
Prize diploma.
PoS
But I mean, the text of the
thesis would be something--
Patashinski
But I don't have here the text
of the thesis. A copy or two have to be kept in Moscow, in the Lenin
Library. There were ideas in the thesis that I had never published, for
example a study of the mechanism of how the interaction is screened out at
an intermediate scale and allows the critical exponent not to be 3/2. I had
at least one good and attentive reader of my thesis, Sasha (Alexander)
Migdal, who read the thesis in the Lenin Library, and used some ideas in a
paper, published 1968 or 1969, about what appeared later to be tri-critical
points.
PoS
He was your official opponent?
Patashinski
No. My official opponents were Tolya Larkin, Ilya
Michailovich Lifshitz, and Michail Alexandrovich Leontovich. Sasha Migdal and
Sasha Polyakov are 9 years younger than I am. I received my degree in 1968, well ahead of them. We
were rather friends at that time with Sasha and his father, A. B. Migdal. In the USSR in these times,
publishing space was considered in short supply, and publications were
asked to be brief. A significant part of what you were doing was not described
in detail, you just tell it to your colleagues. I actually liked it this way,
a collective life and work in Science. There are some of my old preprints
that I would like to have now. They were never published in any journals.
To understand the situation of
that time, you have to keep in mind that our work, and the first
publication of our theory, became a thing of hate and love. There were
those who would support the theory, and those who opposed.
PoS
When you say the first
publication, which one do you mean?
Patashinski
Our presentation in May in
Odessa, the discussion of 1963-64, and the JETP paper in 1964. Actually, there
was an earlier publication, a preprint in 1963, it had the formal status of a
small book. It had mainly the same content as the publication.
PoS
Would that have been a preprint
issued by your Institute or by Pokrovsky's institute?
Patashinski
As far as I can recall, by my
Institute. This was a new practice, the way it was published gave it the
status of an official publication. It had a price of 6 kopeks, and you had to
send copies to libraries, including a mandatory copy to the Lenin Library. As far as I
remember, it was this publication in 1963, and only then was a paper sent,
probably in August of 1963, for publication in JETP, and somewhere in 1964
it was printed by JETP.
The last paragraph of this
first paper answers two questions we were asked at this time. One question
is about the relation to the Kolmogorov theory of turbulence. Kolmogorov
proposed, ad hoc, scaling laws for developed hydrodynamic turbulence. In the last paragraphs of our paper,
we compared our statistical mechanics theory, and the Kolmogorov theory of
turbulence. I tried to expand this line later, in a talk given at the
International Symposium of Many-Body Problems held in Novosibirsk in 1965,
and in later publications on turbulence.
PoS
Can we go back, in terms of
formulating the problem, you were out to prove singularities in the
partition function or whatever. That was the big thing.
Patashinski
We did not used partition
function in the first paper. As you know, to describe nature, you need a mathematical
language. There are usually possibilities to use different languages to
describe the same basic physical phenomena. For example, in quantum
mechanics you have the matrix mechanics of Heisenberg, the wave mechanics
of Schroedinger, Feynman path integrals, and other equivalent methods, to
describe the same reality. In the theory of fluctuating fields, which
includes high energy theories, statistical turbulence, statistical physics,
phase transitions, and other systems, there is a language of correlation
functions, or Green functions, and there is another language of
distribution functions which was not too popular in critical phenomena
until Leo Kadanoff actually brought it into the theory, although in the
Landau and Lifshitz Statistical Physics, the Ornstein-Zernicke theory is
derived using the distribution function language. Kolmogorov used correlation
functions and formulated scaling (or similarity, as it was called) in
turbulence in terms of correlation functions. We used the same language to study critical phenomena
and formulate critical point scaling (self-similarity of long wavelength fluctuations
at different length scales). The importance and advantages of considering the probability
distribution became clear due to the work of Leo Kadanoff. I think that
what Leo did is much more important than scaling by itself -- he gave a new
twist, a new way of thinking about field-theoretical problems. I was very
disappointed when I did not see Leo's name sharing the Nobel Prize for the
Renormalization Group with Kenneth Wilson. Wilson certainly deserves his Nobel
Prize, but it was Leo who actually found the idea of treating the system in
terms of distribution functions and renormalization while changing the
length scale, and formulated scaling in this language.
PoS
Specifically, what is the role
that your paper on liquid helium, with Pokrovsky, plays?
Patashinski
Oh, the answer depends on the point
of view. Different people may have different answers.
PoS
Let me put it this way: your
paper on liquid helium, and then the subsequent one on the superconductor--
Patashinski
And a lot of conference talks
and discussions...
PoS
I mean, it translates Bogoliubov
into the language of Green's functions and correlation functions.
Patashinski
No. Bogoliubov is an important
contribution in Bose gas, but it has nothing in common with scaling. At the
lambda-point,
you don't even need the Bogoliubov transformation, only below the lambda-point.
PoS
It translates, right? It
translates what Bogoliubov had done for liquid helium into the language of
trying to see how you get deviations from free Bose-Einstein. What do
interactions do, how does it relate to...
Patashinski
Let me try to give a more
detailed answer. This is a different task. In physics, in a theoretical
science, to do things you need mathematics. You need a developed
mathematical technique to describe systems and phenomena. And to describe
liquid helium, which is surely not the most simple system in the world, some technique
was developed. First, the model of an ideal Bose-gas. The result was the
Einstein-Bose condensation. Then one asks what happens when you have interactions, how this
modifies the Bose-Einstein condensate. There were many attempts to understand
what happens, not at the lambda-point, but at zero
temperature, in the ground state of the system. An important step here was
made by Bogoliubov, a special realization of the Landau idea of symmetry
breaking. This step was not a solution of the lambda-point problem, and if
the understanding would remain at the level of Bogoliubov work, we would
have to do first the work of Matsubara, and Belyaev, and many others, and
that would take a lifetime.
It was important that Matsubara
and then Belyaev and others found a regular way of treating the
Bose-liquid problem perturbatively in terms of some kind of series
expansion. Bogoliubov is the
first approximation in this theory. The critical region is where the perturbation
theory fails to give results, because there is no small parameter you can
use. Outside of the
critical region, there was a technique of resuming the perturbation series
to use the scattering lengths or gas parameters if they are small. The result
of many studies was a regular language of Green's functions that we have
used in a new way to
describe the fluctuations at the lambda-point. We formulated the problem
in terms used by our colleagues, these terms were correlation functions,
Green's
functions, and so on. Bogoliubov
was very important because he had found a way to get the first correction
to the ground state of an ideal gas for the case of a weak interaction, but
his work is not a solution of the lambda-point problem.
PoS
No, I agree. But I'm trying to
understand, if you have a notion of correlations near the phase transition,
right, that correlation length becomes infinite.
Patashinski
In this question, I can rather
refer to the Landau and Lifshitz Statistical Physics. The Ornstein-Zernicke
theory -- they actually made the first step in critical fluctuations. It
was created almost a
century ago, and this is a theory of density fluctuations near the critical
point. In this theory, the
correlation function is calculated explicitly, and the correlation length
becomes infinite in the critical point. Ornstein and Zernicke calculated,
in an equivalent to a mean field approximation, the amplitude of
fluctuations, and the correlation function. This was a large step forward.
The statistical mechanics has a general relation between fluctuations and
susceptibilities, it's a special case of what's called
fluctuation-dissipation theory. The general case deals with dynamic response
and time-dependent correlations, but there is a special static analogue.
For example, the heat capacity is
proportional to the mean-square fluctuation of energy, and so on. You can
write the susceptibility in
terms of an integral of the pair correlation function. This was a way of
deriving relations between exponents in the behavior of various
thermodynamic properties, widely used before scaling, for example, in the
publications of Michael Fisher. This approach gives useful general relations
between susceptibilities and pair correlation functions. This is not
scaling, but useful general stuff. Scaling, the new discovery and the reason
why it is interesting, is
a special and uncommon regime of fluctuations in a field-theoretical
system. The critical system yields special relations between irreducible
correlation functions of all orders, as found in our work, or, equivalently
but in a different language, it is a non-Gaussian fixed point as it was
formulated by Kadanoff and Wilson. Scaling is a complex phenomena, it has
many facets to understand and describe, and you discover different parts
of the rather complex building
by using different languages as tools. Our language of Green's functions
was for those who know
the field theory, and Matsubara and Feynman diagrams, and Green's
functions. This knowledge was
a norm in the Landau School. You
had to pay a toll of education before you understand what's going on. The
new language Leo brought to this problem was so much simpler and transparent,
and it was much easier to penetrate, so it immediately attracted a lot of
people to the field. An intensive work of many scientists was needed to
reveal the many sides of scaling, and it took several years of this, rather
collective, work to get to the point we are now. Although communication
was a problem, at least for us in the USSR, this was a collective international
work. In the 1960s and beginning of
the 1970s, our American colleagues were frequent guests in the USSR.
PoS
But there is a claim, I mean,
OK, let me phrase it differently. What would you see as the accomplishment
of your paper with Pokrovsky?
Patashinski
Well, to answer you have to
look at what are the main ingredients of the theory now. There were few new
things in this paper. Most important was the discovery of the regime of
self-similarity, or scale invariance, formulated in terms of multiple-point
correlation functions as homogeneous functions of their space arguments and
with special relations between exponents. It was not all the sides of scaling, and the idea of how
to calculate the independent exponents was wrong. But this was the first appearance of scaling in critical
phenomena. We understood the
flaw of 3/2 and re-formulated the theory in 1965 by abandoning calculation of
independent exponents and describing the scaling regime in physical terms;
about the same time and independently Kadanoff published his formulation in
explicitly renormalization group terms.
But, in these 1965-66 papers we,
and Leo, rather better described the new regime, while in the first paper
we discovered this regime and were very concerned to understand how this
regime may happen. An entry part of this was an understanding, although not
a rigorous proof, of how the critical fluctuations in a real system are
reduced to a fluctuating system of classical wave fields. This was expected, as Anderson once
pointed out in his book, but still we found a way to show to ourselves and
maybe also to others that, under certain assumptions, the singular
long-wave part universally separates from the system of interactions into a
universal and simple model of an interacting wave field. This separation takes place only
close to the critical point, where the strongly fluctuating long-wave part
becomes independent from details of the interaction, and becomes independently determined by its
own, internal, nature. In later works, this was extended into the concept
of universality classes of singular behavior. We had a discussion of that feature of our theory in
1963 in Moscow with Paul Martin, who paid special attention to this new feature. He agreed that this is an
aesthetic argument in favor of the theory. It was understood that the singularity is self-tuning,
and when you change details, the change is absorbed by the system because
the singularity has this self-adjustment mechanism.
The scale invariance in the
first work was discovered in an attempt to make ends meet. A power-law dependence
of one-particle Green's function (giving the state occupation number) was
assumed from the beginning. Then it has to be justified. A perturbation theory
approach did not
work because everything diverged. We resummed diagrams to the extreme
extent, exterminating all possible tracks of 'bare' functions, to deal with
physical quantities instead of fictive non-perturbed functions. It was a
hypothesis that was suggested by the structure of the equations that the
n-point
irreducible correlation functions are homogeneous functions of their space
(or Fourier) arguments, with some exponents characterizing the change of
a function when you change the length scale. This homogeneity is, so to
say, the entry step into
scaling, it is some scaling but more general than the special case that we
got at the end. With this form
of correlation functions, we tried to further balance the equations for
n-point correlation functions by a self-consistent treatment, and here we
discovered the relations between exponents that are consistent with the
balance. We had not proven
scaling rigorously, and this task is not done up to now. We just found a
strange but most natural behavior that was not possible to exclude. All
other behaviors seemed to be contradictory. The regime that was thus found,
with
all multiple-point correlation functions as homogeneous functions, and their
exponents bound by our formulas, is scaling formulated in terms of correlation
functions: in Kadanoff and Wilson's terms, this means a non-Gaussian fixed
point. The word "scaling" does
not have a one-word Russian analog; following Kolmogorov, we called the
discovered feature of fluctuations "self-similarity." This regime was the
main new element in this first paper. This first work had flaws, and we attempted
to do too much at once, but we had not found a right way to calculate exponents,
and kept the wrong
approximation for them. But
this first work initiated scaling. The flaws were soon understood, and the
problem became to find a way to get critical exponents, or at least separate
scaling from this task of
calculating exponents. This
was done in our second paper, and independently by Kadanoff.
In the work that followed the
first paper, the equations that determine the long-range, singular part of
correlation functions were reanalyzed and reformulated by different
researchers from different points of view and in different techniques, and
better ways to solve the equations were found. We understood that the way
we used to get the index equal 3/2 is wrong. In
an unpublished preprint somewhere in 1963, I found, using exact identities
between Green's functions, that there may be a contradiction with 3/2. The
next step
was to separate the general scaling from calculation of exponents. We succeeded
in this tack the next year, and this is published in the second paper, our
most cited paper on
critical phenomena. About the
same time, Leo Kadanoff found his block construction. Somebody told me later
that soon after returning from the Moscow conference of 1963, Leo started
studying the
problem, and organized a seminar. You know the result. So,
in this two parallel and independent works, scaling has been now described
as a physical property of critical correlations, without attempting a
mathematical proof, and without mixing the scaling properties with calculation
of independent exponents. Soon, Leo and his coworkers published a famous Review about
this, pure-scaling, stage of the theory.
Another extension of the first
work was to modify and solve the field-theoretical equations. The known feature of the classical
wave-field model is that it is an Euclidean version of a relativistic quantum
field theory. Migdal and Polyakov
reconsidered the Dyson equation used in our first paper, and replaced it by
a dispersion relation known in particle physics, and formulated a
bootstrap scheme. The most advanced
form, however, was later found by DiCastro and Jona-Lasinio. They had explicitly
used the field-theoretical Renormalization Group to get a closed system
that was equivalent to equations from the first paper, but with the
advantage of elegancy and transparency, and free from the difficulty we had
with the Dyson equation. Still, no
special technique of calculating the critical exponents was found. In the course of these studies,
people got used to scaling, and, what is important, it became almost clear
that there is a mechanism of screening of the 'bare' vertex.
PoS
Can you be more specific about
when you say scaling relations, what do you mean? Relations between the
critical exponents?
Patashinski
If you mean the relations
between binary correlation functions, correlation radius, and thermodynamic
singularities, the answer is no, these are not the unique scaling
features. The word 'scaling'
has a broad meaning going beyond the scaling theory of critical
fluctuations. Power laws for
binary correlation functions are more general than the scaling realized in
critical fluctuations. For example, similar relations are predicted by the
mean field theory. The values
of exponents, when they differ from those in mean field theory, from
Landau-Ornstein-Zernicke values, are in contradiction with mean-field
theory, but this contradiction shows up only when you try to calculate the
next approximations, beyond the theory. Relations found by Widom to fit experimental data are
more restrictive and related to scaling, but to explain and understand
these relations you have to go to statistical mechanics, and that is to end
up with a special regime that is scaling, or scale invariance, which is the self-similarity
of all-order correlations that I had already described, with all n-point
correlation functions being homogeneous functions bound by special
relations between exponents; an equivalent definition in Kadanoff-Wilson
terms is that scaling is a non-Gaussian fixed point of the Renormalization
Group transformations. It
means that the fluctuations are non-Gaussian at all large length scales,
and a change of length-scale may be compensated by a change
(renormalization) of the fluctuation amplitude. The non-Gaussian here is a
necessary part. If fluctuations become Gaussian, it is a known and usual
case. In the mathematics of
fluctuating fields, violation of Gaussianity at all large length scales is
a signature of a singularity of measure, a violation of a central limiting theorem
of the probability theory.
The scaling and the
non-Gaussian fluctuations realize a self-organized regime of strong
interactions. There are other situations
in physics where we think of strong interactions, and scaling ideas had
significantly influenced these fields, but the situation there seems to be
different. It is believed now
that critical points in two- and three-dimensional systems realize a
perfect scaling case. A similar suggestion is the Kolmogorov 1941 theory of
turbulence, but now people think that something violates the usual scaling
regime in turbulence, and the result is, probably, anomalous scaling, with
different relations between higher-order correlations. So, scaling is not the common case,
something may violate scaling, and we do not know what and how. It may be, for example, that a
vector with Galilean invariance is a different object. In elementary particles theories,
the space-time is 4-dimensional, some theories even go for more dimensions,
and that makes a difference. At the end of the first paper, we mentioned the Kolmogorov theory as
an example of scaling, and
also pointed out, answering Pomeranchuk's question, that 'the number of
space dimensions is an important variable in the problem.'
PoS
This may be in the second
paper, I mean, this is the Bose paper.
Patashinski
The remarks are at the end of
the first paper. To continue:
mathematically you get a very similar, also not coinciding, structure of equations
in many systems, in turbulence, in particle theory. At this point, we do
not know exactly what differences are important. We knew in 1963 that in four dimensions the theory
has logarithmic difficulties, and there is a logarithmic screening of the
initial, 'bare', charge. The
idea of practically using the number of space dimensions as a variable comes
from Wilson's studies. It gave Wilson and Fisher the long-sought small
parameter and a way to get approximate values of exponents. But this was achieved much later,
in the 1970s.
PoS
And your interaction with
Migdal and Polyakov?
Patashinski
In 1963, they were about
18. Later, when they started
as physicists, we became friends. As I told, two different directions of
studies emerged from the first work. There was the microscopic theory --
you should derive everything from the Hamiltonian, prove scaling and find
the exponents. This line of studies was continued by Migdal and
Polyakov. They widely used the
fact that, after a separation
of the the zero-omega parts of Green functions, the resulting wave-field
model became part of a mathematical formalism that treats critical
fluctuations as an Euclidean projection of a quantum field theory. This
unification was known in Feynman diagrams as Weeks turn in the complex
energy-momentum plane, and it follows from causality conditions. Experimental
critical systems are 2- or 3-dimensional, so the corresponding quantum fields
have to be considered in a less-than-four dimensional space-time, unlike
what one has in elementary particles. Later, DiCastro and Jona-Lasinio
used this mathematical feature and
gave a very good and complete formulation of the critical point
problem.
PoS
But they already used renormalization
group, this notion.
Patashinski
Everything that we all were doing was Renormalization Group, explicitly or not explicitly. DiCastro and Jona-Lasinio's work was
the top in the development of this field-theoretical line. Following our
first study, Sasha Polyakov and Sasha Migdal re-examined the structure of the theory, and
used their experience in dispersion relations to formulate what was called
the bootstrap approach. Then,
DiCastro and Jona-Lasinio found a form of the theory that is explicitly a
field-theoretical Renormalization Group, and an interpretation of this form
as simultaneously a particle theory and critical fluctuation theory. They
considered an extended space-time manifold that extends beyond the Euclidean
space of statistical mechanics. All of these works brought no practical idea how to make
calculations. Again, there
were two different directions to continue the first work -- one was microscopic
theory, and the other was general scaling theory based on physical assumptions,
refusing to calculate critical exponents.
About the second half of 1964,
we slowly moved to describe our theory as a physical picture. These ideas brewed, but we became
tired of trying to convince some colleagues that we were on the right track, and
needed a break. I tried some
ideas in high energy and turbulence, and Pokrovsky went to some stochastic
problems. Of course, we both
continued to think about our work. By a pure coincidence, when I visited Moscow, I think, at
the end of 1964, I met Ilya Lifshitz near the Hotel 'Moscow', and he invited
me to have a lunch together. He took me to a café in the Hotel, and, encouraged by his
friendly talk, I just could not resist telling him an idea that I had tried to
pursue for some time, but was afraid to get the same hostile reception I had
became accustomed to. I and
Valery became very tired and felt unhappy fighting with our opponents. Surprisingly, Ilya Michailovich became
very excited and enthusiastic and urged to immediately develop and publish
it. Well, I went back to
Novosibirsk and told Valery -- our respect and even love for Ilya was very
high -- I said 'Valery, Ilya Michailovich appreciated these ideas.'
In a short time, we had
developed these ideas into a theory, later we wrote an article and sent it
to JETP. This work made a
breakthrough in public opinion. Sasha Voronel, who at this time had an offer from Dubna, organized
there an International Conference on neutron scattering. We were invited to present a talk.
This time, I was the speaker; it was, probably, the first time that I was
the speaker for both of us. I
was given a normal time on the plenary session, and delivered my talk, but
what happened was in some way similar to what happened in Odessa in 1963 when
Valery presented our first work. In the course of my talk, and at the end, there were many very
interesting questions, and the audience had shown high interest. This was
in May of 1965, in this year --
PoS
May of 1965? So the conference
was on neutron scattering, and only coincidentally did you--
Patashinski
No, this wasn't a
coincidence. This conference was
organized by Sasha Voronel, and phase transitions were a great part of it. Neutron scattering is a way to study
correlations.
PoS
Patashinski
I think, at the time this was
his legacy in science, to study the critical state and to do this now by
neutron scattering.
PoS
No, why did he invite you to
give this talk?
Patashinski
Well, Valery and Sasha were
friends, and I become a friend with Sasha, too. We had similar goals in
sight, and I hope that he recognized that we were good players in the field.
A large delegation was from the Kharkov School, with Ilya Lifshitz and
close associates like Mark Azbel and Musi
Kaganov, and there also was a representative selection of experimental
physicists from Moscow.
To continue: I made my
presentation, answered a lot of questions, and then a strange thing
happened: the organizing committee took a decision that the next day the
conference would stop the regular schedule, and instead I would have as much time
as I need to present the theory in more detail, and participants would ask
questions and discuss the theory. Next day, I really made a very long talk, a few hours, and answered
many questions. There was a
lot of interest, really inspiring questions were asked by Andrew
Borovik-Romanov. Unlike the
first paper, physical arguments were used to justify the scaling relations
between fluctuations, and using these relations, the reduced variables form
of the thermodynamic potential was derived. The old Landau idea of changing
the expansion parameter and resuming singular terms was used for this
derivation. This work very soon
became our most cited paper. It was a general scaling theory with no
mention of how to get critical exponents. Critical exponents were treated as structural constants.
There was a few months' delay in publication because the referee wanted us to
explain the relations between our theory and the Yang-Lee theorem on partition
function zeros in the Ising model. At this time, Valery was mostly in Moscow and I in Novosibirsk, communications
became slow, so it took some time to add an explanation of this relation.
PoS
This is the 1968 paper
"Similarity hypothesis for correlations in the theory of second-order
phase transitions," Soviet Physics JETP 26 (1968): 1126?
Patashinski
No,
this was the paper , "Behavior of an ordering system near the phase
transition point", Sov. Phys. JETP, 292 (1966); we usually call it the second paper. Another paper with the same ideas, the
first paper on critical phenomena I published without Valery, who moved to
Moscow, was written a month or two later, but was printed earlier, "On
the density correlation near a critical point", Sov. Phys. JETP
Letters 3, 132 (1966). The "Similarity
hypothesis for correlations in the theory of second order phase
transitions", Sov. Phys. JETP 26,
1126 (1968) is the third paper; it was mainly finished about 1966 but later
than the second paper. I tried
to continue working with Valery, but he went to Moscow and started working
on other things. For some time already, Valery had serious health problems
and needed to go to Moscow. We
had plans to move to Moscow together, Valery, Yury Rumer, and I. It so
happened that Valery moved alone, to the Landau Institute. This was a difficult
time for us, many things were delayed. In 1967, I decided to finish alone and publish this
paper. At this time, Kadanoff's
paper has been already published, and had some influence on the final
version, but I found that there were still enough new ideas to publish.
When Valery moved to Moscow and
I remained in Siberia, I felt lonely. After spending so many months working
together, for many hours a day, we had become so used to each other, that
each of us was able to think as
if we were together. In August of 1963, I spent a month in a hospital to
heal my really bad lower back, and Valery went on vacations to some place
in the South. At the time, we
had technical difficulties in formulating the theory for He-4 below the lambda-point,
how to put the Bose-Einstein condensate in our theory without violating the
scale-invariant structure of our theory. This part of the work was missing
in the preprint of 1963 because the preprint was written earlier than August.
Well, in a month, Pokrovsky
returned, and when we met, his first question was, "Have you done
it?" 'Yes, I did. And you?' ' Yes, I did.' And, just for curiosity, he
said, write your equations and I will write mine. We had written the
equations and compared -- and not only the equations were the same, the
notations for all quantities were the same, although there were some newly
appeared things. We became so attuned to each other that we became halves
of a Patashinski-Pokrovsky unit, and it was not possible to separate these
halves without some pain.
PoS
When did you become aware of
what Widom did?
Patashinski
The Widom paper appeared after
the first paper work was done and the first presentations were given. We read his paper probably after
the first paper was written, but we had an opportunity to add a reference
later. It was not easy to get foreign
magazines in Siberia, but Pokrovsky was in Moscow, read the papers of Widom
and of M. E. Fisher, and we discussed them.
PoS
And how does it affect you in
terms of thinking? Because that's--
Patashinski
The paper dealt with relations
between exponents and thermodynamics. Widom found a reduced variable expression for the free energy, and he
found this from experimental data, making some assumptions. In our first work, we were more
interested in correlation functions of high order and how to balance the
entire scheme of the statistical theory. Thermodynamics was something
secondary for us, it had to follow from our equations. So, it had no influence on the
first work, and probably on the second work, too, but the second work dealt
more with thermodynamics, and here we derived what Widom assumed to fit the
experiments. There was
intense effort, probably in relation with Voronel's experimental results, to
assign exponents to every measurable and non-measurable quantity, with
M. E. Fisher as the leader and most active author. It was an activity to measure
exponents, find relations between exponents. We had not participated in this activity and initially
paid little attention to it. We tried to make a statistical mechanics theory. The relations between exponents had
to follow from this theory, and we were probably glad to have them, but they
were considered by us as a condensed form of presenting the experimental
data.
PoS
Can I assume from that that somebody
like, say, [the physical chemist] Semenchenko doesn't play much role in the
discussions?
Patashinski
I did know Semenchenko,
and I doubt Valery did. What
is possible is that his ideas were mentioned to us by somebody, and became
part of our scientific background. As far as I understand, but I am not sure, Semenchenko expressed
some thoughts that fluctuations violate Landau's theory. These ideas
were more convincingly proven by Ginzburg and Levaniuk, who calculated the first
fluctuation correction to the heat capacity, and it diverges in the
critical point.
PoS
That's Semenchenko's earlier
work; he's not actually involved in these disputes in the 1960s?
Patashinski
I remember his name was mentioned,
probably by Strelkov, but there were no contacts or influences. Maybe at this time he had done
something else. At the beginning, the theory was technically rather sophisticated,
so only those at the technical level of the Landau Minimum or something
similar were able to really discuss this situation, and the goal was mainly
to prove or disprove scaling and 3/2. The second paper, the 1966 one, was
much easier to understand, partially because, at the time of this paper,
our entire construction of homogeneous functions and their exponents, and
that it is, at least, consistent with the microscopic theory, became kind
of swallowed. The critics concentrated
on 3/2. The second paper dealt
with physics, without too much of mathematics, and without attempts of
proving scaling. Rather trivial mathematics was used to derive physical
results from scaling. Scaling
by itself, now freed from the 3/2 calculation, became a done thing. The task was now simpler, in spite
of opposition the main ideas became accepted by most of the scientific
community, and due to that, the new version of the theory was immediately
accepted by the community.
About this time in 1965, maybe
few months later, Abrikosov asked me to explain the new work to him, and he
was very positive in the discussion. The recognition became even more
visible when Kadanoff's paper appeared. At the suggestion of Ilya Lifshitz, I
submitted and in 1968 defended my Doctor of Physics and Mathematics dissertation
on scaling. Soon I accepted an invitation, by Andrey Michailovich Budker,
to join the Institute of Nuclear Physics, IJaF. Rumer was already there. I
worked in IJaF, now the Budker Institute, until emigration.
PoS
Do I understand you correctly
that what you take pride in your contribution, and your insight is a
formulation in terms of vertex functions and two-particle Green's
functions, where you exhibit certain general non-linear features between
these objects which now you can make claims to give you, by virtue of the
non-linearity, general properties which reflect themselves in the singular
structure of the free-energy and so on?
Patashinski
The question is what new features
we have in the critical state? What do we need to describe in the critical
point? The statement in the
first paper is that we need the full set of correlation functions. For other parts of the
thermodynamic plane, one usually needs, at large distances, only the binary
correlation function. The
behavior of multipoint correlation functions that was found in the first
paper, or equivalently of the fluctuation characteristics used in the
second paper, indicated a violation of the thermodynamic theory of
fluctuations. This was a new
mathematical situation in fluctuating fields, a case of strong interaction
that self-tunes itself into this regime of long-range statistical
dependency, and a farewell to perturbation theory for this problem. This
was a completely new situation, the non-Gaussian self-similarity. A field
is a point in an infinitely-dimensional space, so mathematically one deals
with random processes in infinite-dimensional spaces. To describe this in a legible way,
you need to project this into a lesser number of degrees of freedom. One way to do this projection is to
consider fluctuations on a chosen length scale. Scale invariance means that on each large scale you see in
essence the same statistical features of fluctuations when you use proper
units for length and for field magnitude. This was the picture in the first
paper that was the most important for the future. The importance of this was understood from the beginning,
although new sides of this picture were discovered and emphasized later,
especially in the work of Polyakov and Migdal, DiCastro and Jona-Lasinio, and
of course Kadanoff and
Wilson. This unusual situation,
found in the first paper, was the main reason why the theory was met with
such a resistance. The abandoned
idea of the first work is the assumption of how technically to get the
critical exponents. This was a
minus, certainly, and this weakened our whole construction. It took a lot of work to find a way
to calculate exponents, including the mentioned famous authors and some
others I have not mentioned, and a lot of understanding and simplification,
and some sacrifices in accuracy. We took on, in the first work, a too heavy load. We did a part
of this work, but more work was still ahead.
PoS
The language, non-Gaussian, is
that already there in 1966, or is that there in 1967?
Patashinski
No, attention to this side came
later, it is a main point in the third paper that I published in 1968. I had some ideas earlier, and I read Kadanoff's paper of 1966. Probably I then tried to re-examine what I knew in terms of what
Leo had done.
PoS
So pre-Leo Kadanoff,
non-linearity plays a bigger role in terms of structure of the--
Patashinski
You see, the phenomena by
itself -- fluctuating fields, fluctuations on all scales -- are so complex
that you cannot see it in one simple way. You have to describe many
features from this side and that side, and your ability to understand and
describe depend on your mathematical background. We used a language which
was a little bit cumbersome but widely used in our community, the language
of correlation functions, homogeneous functions--
PoS
With a single coupling
constant?
Patashinski
We arrived at a theory with a self-tuned
coupling constant, and this involved a very unusual and somewhat
mathematically cumbersome construction. This was probably the first
construction of this type in physics. The tough part was that we were not
in a position to use other's results and had to do everything to the first
time and we did not have time to find the most elegant ways to do it. Due to that, we had to pay the
price of maybe excessive complexity. It took a lot of work, ours and others, to make things simpler and
more elegant. As Tolya Larkin once
pointed out in this connection, we did what was necessary but as good as it
gets. Kadanoff's scheme was much simpler.
PoS
Can you describe the
constructions and what you feel was added?
Patashinski
It's a very direct way of
formulating scaling, and it shows new sides of scaling, the fixed point
features. Initially, Leo wrote
that when you start from Ising, you get the same Ising on each scale. This was wrong, but was soon
corrected. But the idea was good. A corrected version described in a detailed review that Leo and his
many collaborators published soon. Wison took off from there, and developed Leo's ideas to the level of a
regular calculus, with the idea of the fixed point as a way to formulate
scaling. I like the theory,
published by F. J. Wegner, of perturbed fixed points, it gives an
understanding of how new scale-invariant fields appear. It's a very complex phenomena,
scaling and the fixed point, it gives a comprehensive way to describe all
correlation functions and other quantities we dealt with. Our language of correlation
functions, homogeneity, etc., was more difficult to use for some
applications, you had to know a lot before you were able to use it. Leo found a simpler language, and
many new things were understood, or old things reformulated and became
visible. Leo found this way to formulate scaling, but to make his ideas a
working technical tool -- this job was done by Wilson.
PoS
I think from our point of view,
what would be helpful is for us to go over what you have said.
Patashinski
Our 1966 publication overlaps
with Leo's work a lot. The two
theories suggest the same physical picture, this is the picture of our
first work, but these parallel works made no attempts to give a
mathematical proof of scaling or calculate critical exponents. Each description had its
advantages, and was better for some applications.
PoS
I think if we transcribe what
you have said this afternoon, and try to, from our point of view, try to
reconstruct the history, would you mind if, for example, DiCastro would
comment on what you have said in terms of what did he get out of reading
your paper with Pokrovsky?
PoS
What we're saying is that it's
something we can easily do on the HRST site.
Patashinski
I will be very interested to
see an open and frank discussion. We briefly described our understanding
of the history in our book,
Fluctuation theory of phase transitions. In a review written with
Kogut, and in his Nobel talk, Kenneth Wilson described his interpretation
of the history of Renormalization
Group and, up to some extent, of scaling. He explained that his job initially
was to explain DiCastro and Jona-Lasinio in physical terms for a seminar
led by Widom, and
he mentioned two different approaches, or I say languages, in dealing with
the problem. There are two different approaches, not in physics but rather
in technical means. One is a
field theory approach that studies correlation functions and Feynman
diagram; this was started with our first paper, continued in works of
Migdal and Polyakov, and then DiCastro and Jona-Lasinio. Later, Tzuneto and
Abrahams used this approach to calculate exponents near four dimensions,
and that brought
the field theoretical approach to the same point as the Kadanoff-Wilson Renormalization
Group. But it so happened that the Kadanoff-Wilson approach was first in
getting these exponents.
PoS
Patashinski
The mathematical trick with the
epsilon expansion was very important to get numbers fast. Following discussions with Pomeranchuk
in 1963 after the Odessa meeting, there was an idea that when you go from four
to three dimensions, you get power laws instead of logarithms, that 'the
number of dimensions is an important variable.' But epsilon expansion is only a smart technical
detail. If this technical tool
would not be found, with the use of computers somebody would find a way to
calculate exponents in real space. So this was a matter of time. The values of exponents are
important, but the most important thing is that they exist, and are
determined by the scaling self-consistency in any of the formulations, as a
'nonlinear eigenvalue problem.' For the field theory, I would say the
formulation of DiCastro and Jona-Lasinio is perfect. They had not
calculated exponents, but the scheme is a closed one. You have nothing to
add to this. The development
of the field-theoretical line, from our first paper, through Migdal and
Polyakov's works, got a clear end-form in the work of DiCastro and Jona-
Lasinio. This, however, was
not the end of development. A conformal symmetry was found by Sasha
Polyakov as a generalization of scaling, then a conformal field theory was
developed. It gave a lot of mathematical details of scaling behavior,
especially in two-dimensional systems. Scaling ideas became part of the
field theory in particles and fields, in many new problems not related to
phase transitions. In this
development, you can find the first paper, but not declare a last one.
PoS
Another thing: it would be good to comment on what Voronel was saying in his interview.
Patashinski
Sure, I would like to see what
other people are saying. Everybody is entitled to his own point of view. And, it's very hard
to make corrections in those points of view. Your understanding of what you
have done many years ago could strongly depend on the development in later
times. Galilean invariance was not invented by Galileo. Clearly, scale invariance had a
latent period after our first publication, there was a latent period when
everybody tried to understand what is right and what is not. Our second paper, and the work of Leo,
and then of Polyakov and Migdal, and DiCastro and Jona-Lasinio, and finally
Wilson, were stages of the theory that followed. I think it is still not all, and new developments will
follow. There can be the first
paper, but hardly the last one--that will be too sad to have the really last
paper.
PoS
It may be the case that it's
not so much an issue of what's wrong and what's right as much as what do
people take away from reading your paper -- they may have read something
different than possibly you intended.
Patashinski
I agree. But what you take is a function of
your knowledge and expectations. As we know from the history, it is not easy to convince people to
accept what you are doing when that is not what they expect.
PoS
Well, with your permission,
we'll conclude now, and we'll continue this conversation online.
Patashinski
I'm glad that the history of
this time has become a subject of study. I had a feeling that, as it happens, many things will be lost or forgotten,
and the next generation will have no interest and no way to know details.
I am glad that this appears not the case for the history of scaling.
PoS
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