Critical Phenomena

Proceedings of a Conference
Held in Washington, D.C., April 1965

(National Bureau of Standards Miscellaneous Document 273, December 1966)

In April 1965 two hundred scientists from eleven countries met in Washington for what participant Cyril Domb later dubbed "the founding conference of critical phenomena." This appears to have been the first time that such a diverse array of specialists gathered under the single rubric of critical phenomena. In the Introduction (PDF) to the published proceedings, conference organizer Melville Green suggested four recent developments that helped motivate this ambitious undertaking:

1) Plausible theoretical predictions of non-classical phase transitions were finally extended successfully from two dimensions to three using painstaking series expansions.

2) The experimental demonstration that even classical fluids can exhibit sharp singularities in the specific heat at the critical point.

3) The use of NMR techniques to show strong similarities between ferromagnetic and liquid-vapor transition phenomena.

4) The experimentally confirmed breakdown of the classical Ornstein-Zernike theory of critical opalescence.

Green emphasized the diversity of the research agendas represented at the conference, which brought together scientists who seldom had occasion to interact with each other. Central to their discussions was the debate over the true nature of critical singularities, and the central premise of the conference itself: in what senses are the various critical phenomena truly like each other?

Keynote speaker George Uhlenbeck applauded the search for universal non-classical behaviors fostered by the cross-disciplinary exchanges of the conference. He was under no illusions about the immediate renunciation of classical mean field theory, however. What Uhlenbeck was searching for was "the reconciliation of Onsager with van der Waals," the synthesis of theories of short-range forces with theories of long-range forces. Hints of the possibility of reconciliation can be found in the subsequent talks, though much of the historical interest of these documents lies in the disagreements about how to achieve that outcome. Readers are invited to comment on the papers and their role in the reader's own work, particularly with respect to "critical phenomena" as a constitutive disciplinary label.

The electronic documents are set up so that you can page through the conference proceedings quickly and efficiently (see the title page, for example). If you prefer, you may also download the scanned documents as PDF files, for which you will need the free version of Adobe Acrobat Reader. You may search the PDF versions for names and terms, but not formulas or chemical nomenclature.

Table of contents

To read individual papers, see the session headings below. The following general topics were addressed at the conference:

• Equilibrium critical phenomena in fluids
• Critical phenomena in Ferro- and antiferromagnets
• Logarithmic singularities
• Elastic scattering
• Inelastic scattering
• Transport and relaxation phenomena

More than thirty papers were presented at the conference (including a supplementary session), with active participation in the session discussions by many in attendance. To see who attended the conference, check the List of Participants.

Equilibrium critical phenomena in fluids

Chairman: A. M. J. F. Michels
G. E. Uhlenbeck — The Classical Theories of the Critical Phenomena (Read paper) (Download PDF)
R. H. Sherman — The Coexistence Curve of He3 (Read paper) (Download PDF)
J. S. Rowlinson — Critical States of Simple Fluids and Fluid Mixtures: a Review of the Experimental Position (Read paper) (Download PDF)
E. H. W. Schmidt — Optical Measurements of the Density Gradients Produced by Gravity in CO2, N2O, and CClF3 Near the Critical Point (Read paper) (Download PDF)
M. E. Fisher — Notes, Definitions, and Formulas for Critical Point Singularities (Read paper) (Download PDF)
Discussion (Read remarks) (Download PDF)

Critical phenomena in Ferro- and antiferromagnets

Chairman: H. B. Callen
C. Domb — Critical Properties of Lattice Models (Read paper) (Download PDF)
G . B . Benedek — Equilibrium Properties of Ferromagnets and Antiferromagnets in the Vicinity of the Critical Point (Read paper) (Download PDF)
W. P. Wolf — Experimental Studies of Magnetic Ising Systems Near the Critical Point (Read paper) (Download PDF)
D. T. Teaney — Specific Heats of Ferro- and Antiferromagnets in the Critical Region (Read paper) (Download PDF)
P. Heller — Nuclear Resonance Studies of Magnetic Critical Fluctuations in MnF2 (Read paper) (Download PDF)
Discussion — (Read remarks) (Download PDF)

Logarithmic singularities

Chairman: C. N. Yang
W. M. Fairbank and C. F. Kellers — The Lambda Transition in Liquid Helium (Read paper) (Download PDF)
M. R. Moldover and W. A. Little — The Specific Heat of He3 and He4 in the Neighborhood of Their Critical Points (Read paper) (Download PDF)
M. H. Edwards — The Coexistence Curve of He4 (Read paper) (Download PDF)
T. Yamamoto, O. Tanimoto, Y. Yasuda, and K. Okada — Anomalous Specific Heats Associated with Phase Transitions of the Second Kind (Read paper) (Download PDF)
H. A. Kierstead — The Logarithmic Anomaly in the Pressure Coefficient of Helium Close to the Lambda Line (Read paper) (Download PDF)
M. J. Buckingham — The Nature of the Cooperative Transition (Read paper) (Download PDF)
Discussion — (Read remarks) (Download PDF)

Elastic scattering

Chairman: P. Debye
P. Debye — Introductory Remarks (Read paper) (Download PDF)
M. E. Fisher — Theory of Critical Fluctuations and Singularities (Read paper) (Download PDF)
H. Brumberger — Scattering of Light and X Rays from Critically Opalescent Systems (Read paper) (Download PDF)
B. Chu — Experiments on the Critical Opalescence of Binary Liquid Mixtures: Elastic Scattering (Read paper) (Download PDF)
Discussion — (Read remarks) (Download PDF)

Inelastic scattering

Chairman: K. S. Singwi
W. Marshall — Critical Scattering of Neutrons by Ferromagnets (Read paper) (Download PDF)
L. Passell — Critical Magnetic Scattering of Neutrons in Iron (Read paper) (Download PDF)
O. W. Dietrich and J . Als-Nielsen — Critical Neutron Scattering from Beta-Brass (Read paper) (Download PDF)
N. C. Ford, Jr., and G. B. Benedek — The Spectrum of Light Inelastically Scattered by a Fluid Near Its Critical Point (Read paper) (Download PDF)
S. S. Alpert — Time-Dependent Concentration Fluctuations Near the Critical Temperature (Read paper) (Download PDF)
Discussion — (Read remarks) (Download PDF)

Transport and relaxation phenomena

Chairman: R. W. Zwanzig
J. V. S e n g e r s — Behavior of Viscosity and Thermal Conductivity of Fluids Near the Critical Point (Read paper) (Download PDF)
M. Bloom — Nuclear Magnetic Resonance Measurements Near the Critical Point of Ethane (Read paper) (Download PDF)
D. Sette — Ultrasonic Investigation of Fluid System in the Neighborhood of Critical Points (Read paper) (Download PDF)
C. E. Chase and R. C. Williamson — Ultrasonic Investigation of Helium Near Its Critical Point (Read paper) (Download PDF)
C. W. Garland and K. Renard — Ultrasonic Investigation of the Order-Disorder Transition in Ammonium Chloride (Read paper) (Download PDF)
Discussion — (Read remarks) (Download PDF)

Supplementary session

H. I. Lorentzen and B. B. Hansen — Effect of Gravity on the Equilibrium Mass Distribution of Two-Component Liquid Systems. The Observation of Reversed Diffusion Flow (Read paper) (Download PDF)
S. Katsura and B. Tsujiyama — Ferro- and Antiferromagnetism of Dilute Ising Model (Read paper) (Download PDF)
S. F. Edwards — The Statistical Mechanics of a Single Polymer Chain (Read paper) (Download PDF)
I. M. Firth — Some Comments on Techniques of Modern Low Temperature Calorimetry (Read paper) (Download PDF)