The Statistical Mechanics of Phase Transitions

Abstract This article traces the development and study of phase transitions from late last century to the present day. We begin with a brief historical sketch and a description of the statistical mechanics of phase transitions. Particular attention is given to the modern era which began in 1944 with Onsager's celebrated solution of the two-dimensional Ising model. Points of development since Onsager, which are highlighted in this article, include the study of critical exponents, the scaling hypothesis, realisation of the universality of critical exponents and the recent renormalization group approach to critical phenomena. The basic idea of the renormalization group method, rather than the detailed application of the recipe to particular cases, is stressed and is discussed critically in some detail.

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