Critical behavior of random-bond Potts models

The effect of quenched impurities On systems undergoing 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 explains the absence of any latent heat in 2D, and suggests that for d > 2 such systems exhibit a tricritical point with an exponent nu related to those 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 ratio beta/nu which varies continuously with q, and a weakly varying exponent nu approximate to 1. We find strong evidence for the multiscaling of the correlation functions.