Phase transitions in two-dimensional random Potts models

TL;DR

This paper reviews how uncorrelated quenched disorder affects phase transitions in two-dimensional Potts models, combining theoretical, numerical, and conformal invariance methods to explore universality and symmetry properties.

Contribution

It provides a comprehensive analysis of disorder effects on 2D Potts models, including validation of conformal invariance and insights into replica symmetry breaking.

Findings

Disorder can change the order of phase transitions in 2D Potts models.

Conformal invariance methods are validated in disordered systems.

Evidence for or against replica symmetry breaking was analyzed.

Abstract

The influence of uncorrelated, quenched disorder on the phase transition of two dimensional Potts models will be reviewed. After an introduction where the conditions of relevance of quenched randomness on phase transitions are exemplified by experimental measurements, the results of perturbative and numerical investigations in the case of the Potts model will be presented. The Potts model is of particular interest, since it can have in the pure case a second-order or a first-order transition, depending on the number of states per spin. In 2D, transfer matrix calculations and Monte Carlo simulations were used in order to check the validity of conformal invariance methods in disordered systems. These techniques were then used to investigate the universality class of the disordered Potts model, in both regimes of the pure model phase transitions. A test of replica symmetry became possible through a study of multiscaling properties and a detailed analysis of the probability distribution of the correlation functions was also made possible.