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 ν related to those of the random-field model by ν0ex0ex=0ex0exνRF/(2-αRF-βRF). In 2D we analyze the model using finite-size scaling and conformal invariance, and find a continuous transition with a ratio β/ν which varies continuously with q, and a weakly varying exponent ν≈1. We find strong evidence for the multiscaling of the correlation functions.