Scaling concepts in describing continuous phase transitions

Abstract

Phase transitions, like the boiling of water upon increasing temperature, are a part of everyday experience and are yet, upon closer inspection, unusual phenomena, and reveal a host of fascinating features. Comprehending key aspects of phase transitions has lead to the uncovering of new ways of describing matter composed of large numbers of interacting elements, which form a dominant way of analysis in contemporary statistical mechanics and much else. An introductory discussion is presented here of the concepts of scaling, universality and renormalization, which forms the foundation of the study of continuous phase transitions, such as the spontaneous magnetization of ferromagnetic substances.