A unified picture of continuous variation of critical exponents

Indranil Mukherjee, P. K. Mohanty

Published 2023-07-27Version 1

Renormalization group (RG) theory allows continuous variation of critical exponents along a marginal direction (if any) but does not predict the functional form. Recently it was proposed that continuous variation must occur in a way that leaves scaling relations invariant. For magnetic phase transition, the variation can occur in three different ways: I. $\gamma$ varies keeping $\delta$ fixed, II. $\delta$ varies keeping $\gamma$ fixed and III. both $\delta$ and $\gamma$ vary. In this article, we study the isotropic Ashkin Teller model on a two-dimensional square lattice and show that the magnetic and electric phase transition along the self-dual line exhibit continuous variation of critical exponents which are of Type-I (formally known as weak universality) and Type-III respectively. We show that the scaling functions of both electric and magnetic phase transition are only a scaled version of the universal scaling function of the Ising universality class in two dimensions.