Nonuniversality in random criticality

TL;DR

This paper uses scale invariant scattering theory to demonstrate a line of RG fixed points in coupled 2D Ising models with quenched disorder, revealing nonuniversality in random critical systems.

Contribution

It provides an exact theoretical analysis of coupled disordered Ising models, highlighting nonuniversality and connecting to previous perturbative and numerical studies.

Findings

Existence of a line of RG fixed points for N ≠ 1

Nonuniversality in critical behavior of disordered systems

Potential relevance to Ising spin glass and other random critical phenomena

Abstract

We consider $N$ two-dimensional Ising models coupled in presence of quenched disorder and use scale invariant scattering theory to exactly show the presence of a line of renormalization group fixed points for any fixed value of $N$ other than 1. We show how this result relates to perturbative studies and sheds light on numerical simulations. We also observe that the limit $N\to 1$ may be of interest for the Ising spin glass, and point out potential relevance for nonuniversality in other contexts of random criticality.