Physics of Scale Activities

Cyril Domb Interview

Cyril Domb Interview

Due to a failure of the recording equipment the following is the reconstruction of the interview of Prof. Cyril Domb by S.S. Schweber on June 10, 2002 in Prof. Domb's apartment in Jerusalem, from the notes taken by S.S.S.

I was born on December 9, 1920 in London into an orthodox Jewish family that had emigrated from Galicia, Poland. My mother's parents were very influential in my upbringing. My parents were of modest means and I attended an ordinary public school for the first six years of elementary school. I had there an extremely good teacher -- by the name of Mr. Abrahams -- who spotted that I had an aptitude for mathematics. He tutored me and taught me a little calculus. I am very grateful to him. I went to Hackney Downs secondary school. Hackney Downs was not a "fancy school". Fancy schools trained their students for scholarships to go either to Cambridge or Oxford after matriculation-- Fred Hoyle, who I met later, called the products of the fancy school "trained greyhounds." But the school had an outstanding mathematics teacher -- F.J. Swann-- who gave me the books needed to study for the mathematics examinations. I had a scholarship that allowed me to get along very well and thus I could study free of concerns. The 6th form is usually a two year course and one takes the examinations at the end of the second year. But Swann suggested that I take the December examinations -- which I did. To get a scholarship one usually needed to do well on 6 out the 10 questions. I had studied the geometry books of Winchester's famous math teacher, Clement Durell, and I did very well on the geometry questions of the exam -- well enough to be awarded a fellowship to Pembroke. I went up to Cambridge -- Pembroke -- in October 1938. The head tutor at Pembroke, Wynn, was a clergyman who was very helpful. He could have excused me from the College as I was an observant Jew -- but he felt that it was important that I partake of that part of College life. I did so as he arranged that I would get vegetarian meals.

During my first year at Cambridge my tutor was Stoneley, a quite good geophysicist who later became a FRS. I took a course in linear algebra from Philip Hall -- and his lectures were so outstanding that I used my Pembroke notes for the course on linear algebra that I gave at Bar Ilan a few years ago. I got a first class for the work during my first year at Pembroke. World War II broke out in September 1939, just before I started my second year at Pembroke. That year I worked mostly by myself and at the end of the year I took the math tripos and did very well ; I finished as a wrangler.
During my third year I attended mostly graduate lectures. I listened to Dirac, whose presentations were the same as his book. Eddington, whose lectures on general relativity I attended, was a poor lecturer. I studied wave mechanics from Frenkel's book and statistical mechanics from Fowler's book. Incidentally, Fowler was around but was doing war work. I did reasonably well in part III and graduated from Cambridge in the summer of 1941. As the war was on, Stonely said to me "To do something for the war effort you should do applied mathematics and return to pure mathematics after the war is over.

I graduated from Pembroke in June 1941. In July I joined the research group on radar at the Admiralty Signal Establishment (ASE)in Portsmouth. Since there were no "theory" groups at ASE I was appointed as a temporary experimental assistant and assigned to do practical work. Also assigned to the experimental group was Fred Hoyle. Since both of us were particularly inept with a soldering iron we were sent off to a hut on the outskirt of the ASE and told to concern ourselves with theoretical matters. Hoyle was 26 at the time and a Junior Fellow at St. John's in Cambridge. He had an "ebullient" personality and was very original. His area of research was astrophysics and he tried to convince me to become an astrophysicist. He did not succeed as I was then already persuaded that my own interests were in statistical mechanics and solid state physics. Incidentally, Hoyle did not switch off thinking about physics during the war. Meeting him, working with him was a "very significant point in my career." Herman Bondi joined the group in April 1942 and soon thereafter Tommy Gold did so. It was then reconstituted as a "Theoretical Group" with Hoyle as its head and Bondi as deputy. Both Bondi and Gold were born in Austria and had emigrated to England. Both had gone to Cambridge where Bondi had distinguished himself. After the war had broken out both had been interned on the Isle of Man as enemy aliens but were released when their scientific skills and their political views were brought to the attention of the proper authorities by Hoyle. Bondi was a superb mathematician, in contrast to Tommy Gold who was less adept at mathematics but was a superb physical thinker as well as a very good experimentalist. Tommy had three great ideas while at ASE: he designed a screwdriver with a ratchet; later, working with Pumphrey, a fine biologist who worked at ASE, he devised various experiments which helped decipher how the human ear works and corroborated that Helmholtz' view that the ear could be modeled by highly resonant circuits was probably correct; and together with Bondi and Hoyle came up with the idea of the steady state universe. I might mention that all four of us were eventually elected FRS (Fellows of the Royal Society).

One of my first researches at ASE stemmed from a problem that had been posed to Fred Hoyle by the Navy. Receivers operating with 7 meter wavelength radar could detect enemy aircraft at a satisfactory range but there was no indication of their height. Could a method of height estimation be suggested. Hoyle devised a practical, successful solution. When shorter wave length radar became available a new method had to be devised which required a simple and accurate calculation of the field strengths at any given height above the surface of the earth of the radiation emitted by a radar transmitter. G.N. Watson had solved the problem of the diffraction of an electromagnetic waves by a sphere of radius R. His solution was valid for R being greater or smaller than the wavelength of the radiation, but could not readily be used for practical calculations of the propagation of electromagnetic waves around the earth. M.H.L. Pryce -- who had joined the ASE at the same time as I had and whom I met a few months thereafter -- had produced an elegant and useful perturbative solution in the case in which the dependence of the field strengths on the electrical characteristics of the earth is negligible. In particular, for wave lengths from the infrared up it is then to correct to calculate as though the earth or sea were a perfect conductor. He had suggested that for diffraction around the earth an effective and justifiable approximation consisted in using a metric that took into account only terms to first order in the curvature. Solving Maxwell's equations with this metric led to solutions expressed in terms of Airy integrals. Pryce sent me to J.P.C. Miller at Liverpool University to compute values of the Airy integral for complex values of its argument. Miller had tabulated the values of the Airy integral for real values of its argument, but Pryce's solution required its values along certain lines in the complex plane. I completed the calculations and Pryce and I produced a set of curves from which the field strengths at any distance from a radar transmitter could readily be derived. It was a very useful introduction to getting numerical answers from series expansions. I wrote up our joint work as an A.S.E. report in September 1942. It was circulated on both sides of the Atlantic: in the UK and in the United States and the curves that were featured in the report were widely used. After the war I rewrote the report for publication in the Journal of the Institution. It appeared in Volume 94, Part III, No. 31, in the September 1947. Its title was "The Calculation of Field Strengths over a Spherical Earth." The Admiralty sent us a letter of appreciation upon its publication.

I got engrossed in probability theory through my work at ASE. I there became interested in the scattering of electromagnetic radiation from rain clouds. And in particular the scattering of em waves with wavelengths from 3cm to 1 meter (radar), as well as longer radio waves. When the spacing between the raindrops is large compared to the wave length of the radiation the droplets can be treated as random scatterers, whereas when the wave length is large compared to inter-droplet separation the cloud should be treated a continuous medium with a dielectric constant different from 1. Can one describe the transition from the"incoherent" regime to the "coherent" one? Consideration of this problem led me to the study of a special type of random walk, and to my first scientific publication: "The resultant of a large number of events of random phase". Proc. Cambridge Phil. Soc. 42(1946): 245-249. Coulson criticized the paper, but in a reply to his objections (Proc. Cambridge Phil. Soc. 43(1947): 587-589 )I showed that the formula I had derived was adequate for the applications with which I had been concerned. Working at ASE is what initiated me to problems in probability, and probability became central in my scientific concerns. Bondi did a lot of important work on the statistical distribution of noise in radar receivers which I studied carefully. He and I were supposed to write a book on noise -- but it never materialized.

In June 1945, after the defeat of Nazi Germany, Fred Hoyle went back to St. John's in Cambridge. After V-E day Bondi returned to Trinity and Gold eventually received a Trinity fellowship based on his work with Pumphrey. Unfortunately I had nothing specific. Pembroke College however came through. a very able physics graduate student , Efraim Nahum, had been killed during the only aerial bombardment of Cambridge during the war and his parents had established a scholarship at Pembroke. The College awarded me this scholarship. Money had accrued for three years and it turned out that the amount was enough to support me from January 1946 till September of that year -- at which time it was hoped that I would be awarded a government grant.

At Cambridge I was a graduate student in the mathematics department as theoretical physics was part of that department. The post World War II restructuring of British physics departments to include theoretical physics as an important subdiscipline that was initiated by Peierls, Otto Frisch and others who had been involved in wartime research in the United States had not as yet taken place at Cambridge. When I came back to Pembroke I started immediately doing research. I did not go to any lectures. I first worked on the statistics of particle counters, an area where the knowledge and techniques I had acquired at ASE about Laplace transforms analyzing circuits came to good use. This work resulted in several publications [ papers 3-6 of part VII Stochastic Processes of my CV] and initiated an important area of research for me. I also got very interested in lattice dynamics during my time at Pembroke.

Fred Hoyle had agreed to become the supervisor of my Ph.D. dissertation even though statistical mechanics was not one of his active fields of research. At the time he was giving the university lectures on statistical mechanics Fowler having died. I decided to explore what had been done in phase transitions and studied Fowler and Guggenheim's Statistical Mechanics (1939) and read papers by Lennard-Jones on and Devonshire on melting. The books which influenced me the most were J. Frenkel's Kinetic Theory of Liquids which Oxford University Press published in 1946 and Schrödinger's Statistical Thermodynamics which Cambridge University Press published that same year. I read both of them from cover to cover. Schrödinger's little book was amazingly lucid and enlightening and complemented beautifully Frenkel's critical exposition. Frenkel gave insightful assessments of what had been done and needed to be done in many areas of what is now called condensed matter physics.

The Cavendish in 1946 was a very exciting place as both staff and students were coming back after a prolonged absence. Among those returning were Brian Pippard, Martin Ryle, Denys Wilkinson and Tommy Gold. The Kapitza Club as well as the 2V Club resumed their meetings and I attended the lectures presented there. In fact it was a lecture by A.R. Miller at the 2V Club that started me off on my thesis researches. Miller, who was a student of Fowler's, lectured on the Bethe approximation and its application to polymers and other systems. It became apparent to me that for one dimensional spin systems I could solve the problem exactly. I developed the formalism using transfer matrices only to discover that I had been anticipated by Kramers and Wannier, and by Montroll who had written papers on the subject in 1941. a further search of the literature led me to Onsager's 1944 paper and to the 1945 Reviews of Modern Physics paper by Wannier. Incidentally, in July of that year the first postwar International Physics Conference took place at the Cavendish. It was devoted to a review to the state of knowledge in "Fundamental Particles" and in "Low Temperature." In the opening session of the conference Bohr, Pauli, Dirac and Born addressed the difficulties that had been encountered in relativistic quantum field theories. The speakers at the session on low temperature physics were Fritz London, Kurt Mendelssohn , V. Peshkov and Lars Onsager. I did not understand what Onsager was presenting in his talk on "Transition points". But by the time I read the Proceedings of the conference I had studied both his 1944 paper and the one he later wrote with Bruria Kauffman and I was awed by what he had done and admired his work immensely. Onsager's solution worked only for one particular model , and reliable methods were needed to derive the properties of the many other models of interest. I derived transfer matrices for a host of problems -- including the three dimensional Ising model. They all could be reduced to a simple characteristic form with a large numbers of zeros. Philip Hall, whom I consulted about their properties, convinced me that obtaining exact diagonalization was very difficult. Given my experience from ASE I then investigated how series expansions of the partition function at high and low temperature could be used to obtain information about critical behavior. I first investigated series expansions for the two dimensional Ising model in the absence and presence of a magnetic field, and later did the same for other models. This became my PhD dissertation. It was finished in 1948 and I submitted it in 1949. Rudolf Peierls was the external examiner and at the examination he asked me " What happens to the Onsager solution when you have a magnetic field present?." For the zero field certain simplifications obtained and I could derive all the coefficients of the series expansions. But for the non-zero case the situation was very much more complicated and I could only obtain the first few coefficients of the series but this allowed me to estimate the critical behavior of the magnetization. By examining the behavior of the series in the zero and in the non-zero field cases I conjectured that there were no singularities of the partition function for the non-zero field case. Yang and Lee proved this result rigorously in 1952.

I might add here some general observations. My thesis already noted the equivalence of various systems in so far as their critical exponents were concerned. See my 1949 Royal Society paper. [Papers 1 and 2 of II Ising and Heisenberg Model of my list of publications.] The Ising model was not very popular at the time: It was the Heisenberg model that was considered interesting. The Onsager solution was thought to be a mathematical curiosity. The order-disordered model was considered "real".

In 1948, as a result of a sudden change of governmental policy, the Senior Research Award from the Department of Scientific and Industrial Research which supported me was terminated after two years -- the normal duration for them was three years. As I had not applied for any alternative means of support I was facing a very difficult situation. Fortunately it turned out that Maurice Pryce had just been appointed to a newly established Wykeham Chair in Theoretical Physics at Oxford and that Stanley Rushbrooke had been appointed to a readership in theoretical physics there. Rushbrooke's area of research was statistical mechanics and he was a well established figure in that field. I went to Oxford to give a lecture and to inquire whether there might be a place for me there. As there were a large number of students wanting to do theory and given that I had many problems in series expansions that looked promising and because Rushbrooke had thought well of my work and lecture -- he had not thought of series expansions -- Pryce managed to get me an IC Fellowship. At the beginning of 1949 I moved to Oxford.

Simon who was the effective head of the Clarendon was a great influence on me. Lord Cherwell (F.A. Lindemann)was nominally the head but he was in London throughtout the week in the House of Lords, and in fact I never saw him during my entire stay at Oxford. Simon was a benevolent father figure who personally looked after the staff and students of the Clarendon. He was an experimental physicist who knew how to use theoretical physics. He felt that experimental physics "needed guidance." He taught me to be a physicist. In contrast to Pippard who was terribly critical, Simon at the end of any lecture that he heard always asked very mundane questions. It was he who introduced me to members of both the European and the American theoretical physics community : Born, de Boer, Prigogine, Onsager, Elliott Montroll...

Simon had a great interest in the physics of melting at high pressure. In fact Simon had formulated a semi-empirical formula for the melting curve which expressed the equilibrium pressure as a function of temperature and connected the melting curve with the properties of the substance, namely the temperature at which melting normally takes place and the internal pressure of the solid. His interest in these matters got me involved in solid helium. I wrote a paper on that subject that was published in the Philosophical Magazine and I also presented a paper on the problem of melting points at the 1952 Paris Conference on phase transitions. [ see papers 1 and 2 of part IV Melting in my list of publications.] This 1952 conference was the second of a number of meetings which became known as Statphys. Statphys 1 was a small Conference held in Florence in 1949 that I did not attend as it was by invitation only. But Rushbrooke went and reported on my work on series expansions. It was at that conference that Onsager reported on his results concerning the long range order in the two dimensional Ising model. Rushbrooke told me about them upon his return. Statphys2 which dealt with phase transitions was held in Paris in 1952 and Simon saw to it that I get an invitation to it. De Boer and Prigogine were the organizers and I presented two papers: one on the three dimensional Ising model and the other on the theory of the melting curve at high pressures, work that as I mentioned had been stimulated by Simon's researches. At that conference there occurred two incidents that left a deep impression on me. The first was in a session that Rushbrooke chaired. Earlier that year John Maddox -- who later became the editor of Nature -- had announced that he had obtained a solution of the three dimensional Ising model. Elliott Montroll who had heard about Maddox's claim thought it important to invite him to present his solution. Simon then got money for Maddox to come from Manchester to Paris to lecture on his results. At the Wednesday morning session that Rushbrooke chaired Maddox presented his presumed solution which consisted in a three dimensional integral formula, the analog of the two dimensional integral formula that Onsager had derived for the two dimensional Ising model. When he was finished and started erasing the board Montroll said ;"Leave the formula on the board. After Onsager had arrived at his two dimensional solution he immediately thereafter conjectured that the solution for the three dimensional Ising model might be the formula on the board. He tested it by comparing it with exact series expansions for the partition function, and found that the conjectured formula gave the first two terms correctly but failed to reproduce the third. Thus the formula on the board can't be right and is not the solution to the three dimensional Ising model." Rushbrooke thereafter suggested that those present who had a detailed knowledge of the problem should get together to clarify the situation. Maddox during that sub-session discovered an error in his calculation.

The second incident concerned a presentation by Arnold Munster. At the beginning of the conference Simon told me that Munster was presenting a paper in which he claimed that he could prove on very general, statistical mechanical grounds that all first order phase transitions end in a critical point at sufficiently high temperatures. Simon and I had had extensive discussion on whether the melting curve ends in a critical point at high temperatures above which there is continutiry of state, similar to the liquid-vapor transition. There was experimental work by Bridgman that showed no indication of the existence of such a critial point, and Simon himself in 1937 had pointed out that thermodynamic reasoning by itself cannot be sufficient to decide the matter. I had taken a very firm stand in the negative. The reason for this stemmed from my studies of the Bragg-Williams model. Solids possess long range order, fluids do not. The melting point corresponds to the disappearance of long range order, and bears a resemblance to a critical point. But there is no possibility of passing continuously from the solid to the fluid state since long range order cannot disappear continuously; hence we should not expect a solid-fluid critical point. Given my position it was incumbent on me to defend my views in the light of Munster's claim. Munster's presentation consisted in a very large number of slides which he went through at a very rapid pace and concluded with the assertion: "Therefore every first order transition must end in a critical point.". Each slide that Munster had shown had a dense mass of formulae on it -- e.g. fluctuation formulas derived from grand partition free energies -- most of which I had not absorbed, let alone analyzed during the barrage. What was I to do when confronting him? Fortunately I was sitting next to Marcus Fierz and I told him of my quandary. Fierz then stated that Munster was wrong. He pointed out that Munster may have produced statistical mechanical formulae " But since at no point did he introduce a specific model his results are of a thermodynamical nature -- and I am quite sure that this issue cannot be proved by thermodynamics."

Shortly after I came back to Oxford there appeared an advertisement for a lectureship in mathematics at Cambridge and for a Smithsonian fellowship which although it indicate a strong preference that it be held at Cambridge allowed the possibility of staying at Oxford. Hoyle urged me to apply for the lectureship and Simon for the fellowship. I applied to both and was successful in both. Since I felt the time had come for me to get involved in University teaching I accepted the Cambridge lectureship. Although formally the appointment was in the mathematics department I had an office in the Mond which I shared with Dennis Sciama, Oliver Penrose and Aaron Klug. I stayed in Cambridge from 1952 till 1954. In the fall of 1953 an advertisement appeared inviting applications for the chair in theoretical physics at King's College, London. Even though one usually did not apply for such positions unless there was a hint that one's application would be welcome I applied. I was on the short list with four others. It turned out that both Mott and Pryce, who were familiar with my work, were on the selection committee. I did extremely well on the interview and I guess that J.T. Randall, the head of the physics department at King's was favorably impressed for a few days after the interview I received a letter from him informing me that I had been appointed to the chair. My inaugural lecture "Statistical Physics and Its Problems" was an attempt to convey to a lay audience both the promises and the excitement and rewards of statistical mechanical understanding.