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 $d>\mathrm{}2\mathrm{}$ such systems exhibit a tricritical point with an exponent $\nu$ related to those of the random-field model by $\nu ={\nu }_{\mathrm{RF}}/(2-{\alpha }_{\mathrm{RF}}-{\beta }_{\mathrm{RF}})$. 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 $\nu \approx 1$. We find strong evidence for the multiscaling of the correlation functions.