Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena

Suppose we have a simple bar magnet. We know it is a ferromagnet because it is capable of picking up thumbtacks, the number of which is called the order parameter M. As we heat this system, M decreases and eventually, at a certain critical temperature T c , it reaches zero: no more thumbtacks remain! In fact, the transition is remarkably sharp, since M approaches zero at T c with infinite slope. Such singular behavior is an example of a “critical phenomenon.”

[1]  T. D. Lee,et al.  Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model , 1952 .

[2]  R. B. Potts.  Some generalized order-disorder transformations , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[3]  M. Fisher.  The theory of equilibrium critical phenomena , 1967 .

[4]  D. E. Aspnes,et al.  Static Phenomena Near Critical Points: Theory and Experiment , 1967 .

[5]  H. Stanley,et al.  Dependence of critical properties on dimensionality of spins , 1968 .

[6]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[7]  Roman Jackiw,et al.  Introducing scale symmetry , 1972 .

[8]  J. Gunton,et al.  Renormalization group in critical phenomena and quantum field theory : proceedings of a conference,Temple University, May 29-31, 1973 , 1973 .

[9]  Michael E. Fisher,et al.  The renormalization group in the theory of critical behavior , 1974 .

[10]  M. Fisher,et al.  Soluble renormalization groups and scaling fields for low-dimensional Ising systems , 1975 .

[11]  Società Italiana di Fisica,et al.  Local properties at phase transitions : Varenna on Lake Como, Villa Monastero, 9th-21st July 1973 , 1976 .

[12]  Anneke Levelt Sengers,et al.  Critical‐point universality and fluids , 1977 .

[13]  P. Hohenberg,et al.  Theory of Dynamic Critical Phenomena , 1977 .

[14]  J. Als-Nielsen,et al.  Mean field theory, the Ginzburg criterion, and marginal dimensionality of phase transitions , 1977 .

[15]  P. Gennes.  Scaling Concepts in Polymer Physics , 1979 .

[16]  J. M. J. van Leeuwen,et al.  Real-Space Renormalization , 1982 .

[17]  F. Y. Wu.  The Potts model , 1982 .

[18]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[19]  A. Kashlinsky,et al.  Large-scale structure in the Universe , 1991, Nature.

[20]  É. Brézin,et al.  The large N expansion in quantum field theory and statistical physics : from spin systems to 2-dimensional gravity , 1993 .

[21]  The Large N Expansion , 1994 .

[22]  J. Cardy.  Scaling and Renormalization in Statistical Physics , 1996 .

[23]  C. Domb,et al.  The Critical Point: A Historical Introduction To The Modern Theory Of Critical Phenomena , 1996 .

[24]  G. Vojta.  Fractals and Disordered Systems , 1997 .

[25]  H. Stanley,et al.  Cooperative molecular motions in water: The liquid-liquid critical point hypothesis , 1997 .

[26]  Annick Lesne,et al.  Renormalization Methods - Critical Phenomena, Chaos, Fractal Structures , 1998 .

[27]  M. Fisher.  Renormalization group theory: Its basis and formulation in statistical physics , 1998 .

[28]  H. Stanley,et al.  The relationship between liquid, supercooled and glassy water , 1998, Nature.

[29]  R. Mantegna,et al.  An Introduction to Econophysics: Contents , 1999 .

[30]  RENORMALIZATION METHODS: CRITICAL PHENOMENA, CHAOS, FRACTAL STRUCTURES , 2000 .

[31]  Jaan Einasto,et al.  Large scale structure , 2000, astro-ph/0011332.