2000/12/06 by Ronald Dickman, Dickman, Ronald
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Network Analysis Techniques #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0012079
17 pages + 2 figures; based on talk at Ising100 Colloquium, August, 2000
arxiv created 2000/12/06 · openalex publication_date 2000/12/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The name Ising has come to stand not only for a specific model, but for an\nentire universality class - arguably the most important such class - in the\ntheory of critical phenomena. I review several examples, both in and out of\nequilibrium, in which Ising universality appears or is pertinent. The\n"Ornstein-Zernike" connection concerns a thermodynamically self-consistent\nclosure of the eponymous relation, which lies at the basis of the modern theory\nof liquids, as applied to the Ising lattice gas. Debye and Huckel founded the\nstatistical mechanics of ionic solutions, which, despite the long-range nature\nof the interaction, now appear to exhibit Ising-like criticality. The model of\nWidom and Rowlinson involves only excluded-volume interactions between unlike\nspecies, but again belongs to the Ising universality class.\nFar-from-equilibrium models of voting behavior, catalysis, and hysteresis\nprovide further examples of this ubiquitous universality class.\n