Effect of randomness in many coupled Potts models

TL;DR

This paper uses 2-loop renormalisation group calculations to analyze how randomness affects the universality class and phase transition nature in coupled Potts models, revealing different behaviors based on coupling sign.

Contribution

It introduces a generalized model of coupled Potts systems with randomness and demonstrates how disorder influences phase transition types and universality classes.

Findings

Randomness can change the universality class of coupled Potts models.

The model exhibits a first order phase transition rounded by randomness.

Different signs of coupling lead to distinct critical behaviors.

Abstract

Using 2-loop renormalisation group calculations, we study a system of $N$ two-dimensional Potts models with random bonds coupled together by their local energy density. This model can be seen as a generalization of the random Ashkin-Teller model. We found that, depending on the sign of the coupling term, the universality class of the system in the presence of randomness is different. Under particular consideration, this model presents an example of a first order phase transition rounded by randomness.