Critical Behavior of Coupled q-state Potts Models under Weak Disorder

TL;DR

This paper explores how weak disorder affects coupled q-state Potts models, revealing that disorder can decouple models and induce first-order transitions, challenging some existing theoretical expectations.

Contribution

It provides new insights into the effects of weak disorder on coupled Potts models, including the decoupling phenomenon and the violation of the Imry-Wortis argument.

Findings

Weak disorder causes models to decouple.

Disordered models do not relate as previously thought.

Systems with q>2 remain strongly coupled despite disorder.

Abstract

We investigate the effect of weak disorder on different coupled $q$-state Potts models with $q\le 4$ using two loops renormalisation group. This study presents new examples of first order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relations emerge, at a perturbation level, between the disordered $q_1\times q_2$-state Potts model and the two disordered $q_1$, $q_2$-state Potts models ($q_1\ne q_2$), despite their central charges are similar according to recent numerical investigations. Nevertheless, when two $q$-state Potts models are considered ($q>2$), the system remains always driven in a strong coupling regime, violating apparently the Imry-Wortis argument.