Phase transitions and the scaling hypothesis

Abstract

In the vicinity of continuous phase transitions, thermodynamic quantities and correlation functions typically behave as power laws characterized by universal exponents, which are independent of microscopic parameters of a system. The development of the Wilsonian RG in the 1970s was driven by the desire to gain a microscopic understanding of this universality. In this introductory chapter we briefly review the phenomenology of phase transitions, define the critical exponents, and discuss the relevant scaling laws. For a more detailed discussion of these topics, we refer the reader to other reviews and textbooks (Fisher 1983, Binney et al. 1992, Goldenfeld 1992, Ivanchenko and Lisyansky 1995, Cardy 1996, McComb 2004, Kardar 2007). © 2010 Springer-Verlag Berlin Heidelberg.