On the Renormalization Group Explanation of Universality

Abstract

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group (RG). This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a real-space or a field-theoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to be distinguished: while the field-theoretic approach explains universality, the real-space approach fails to provide an adequate explanation.