Tests of conformal invariance in randomness-induced second-order phase transitions

The conformal covariance of correlation functions is checked in the second- order transition induced by random bonds in the two-dimensional eight-state Potts model. The decay of correlations is obtained via transfer. matrix ca lculations in a cylinder geometry, and large-scale Monte Carlo simulations provide access to the correlations and the profiles inside a square with fr ee or fixed boundary conditions. In both geometries, conformal transformati ons constrain the form of the spatial dependence, leading to accurate deter minations of the order parameter scaling index, in good agreement with prev ious independent determinations obtained through standard techniques. The e nergy density exponent is also computed. [S1063-651X(98)50812-4].