Critical Behavior of Random Bond Potts Models

TL;DR

This paper investigates how quenched impurities affect phase transitions in the q-state Potts model, revealing continuous transitions in 2D and proposing a mapping to the random field Ising model to explain critical behavior.

Contribution

It introduces a mapping to the random field Ising model for large q and analyzes the critical behavior of disordered Potts models using finite-size scaling and conformal invariance.

Findings

In 2D, the transition is continuous with a varying magnetic exponent.

The correlation length exponent is approximately 1 across different q.

Evidence of multiscaling in correlation functions is observed.

Abstract

The effect of quenched impurities on systems which undergo first-order phase transitions is studied within the framework of the q-state Potts model. For large q a mapping to the random field Ising model is introduced which provides a simple physical explanation of the absence of any latent heat in 2D, and suggests that in higher dimensions such systems should exhibit a tricritical point with a correlation length exponent related to the exponents of the random field model by \nu = \nu_RF / (2 - \alpha_RF - \beta_RF). In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a magnetic exponent \beta / \nu which varies continuously with q, and a weakly varying correlation length exponent \nu \approx 1. We find strong evidence for the multiscaling of the correlation functions as expected for such random systems.