Critical Behavior of Random Bond Potts Models

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 ν= ν_RF / (2 - α_RF - β_RF). In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a magnetic exponent β/ νwhich varies continuously with q, and a weakly varying correlation length exponent ν\approx 1. We find strong evidence for the multiscaling of the correlation functions as expected for such random systems.