Theory of dynamic critical phenomena

1977/07/01 by P. C. Hohenberg, Bertrand I. Halperin · 96 citations
Earth and Planetary Sciences · Physics and Astronomy · #High-pressure geophysics and materials #Quantum, superfluid, helium dynamics #Theoretical and Computational Physics

paper · doi:10.1103/revmodphys.49.435

openalex publication_date 1977/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of ⁴He.

Citations

• Existence of Long-Range Order in One and Two Dimensions
• Hydrodynamic fluctuations at the convective instability
• Scaling Laws for Dynamic Critical Phenomena
• Calculation of Dynamic Critical Properties Using Wilson's Expansion Methods
• The Ising model with a transverse field. II. Ground state properties
• The theory of equilibrium critical phenomena
• Quantum critical phenomena
• Logarithmic Corrections to the Molecular-Field Behavior of Critical and Tricritical Systems
• The renormalization group: Critical phenomena and the Kondo problem
• Generalization of Scaling Laws to Dynamical Properties of a System Near its Critical Point
• Transport, Collective Motion, and Brownian Motion
• Phase Transitions and Critical Phenomena
• The renormalization group and the ε expansion

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