Multiscaling of energy correlations in the random-bond Potts model

We numerically calculate the exponent for the disorder averaged and fixed-sample decay of the energy-energy correlator in the q-state random-bond Potts model. Our results are in good agreement with a two-loop expansion (cond-mat/9910181) around q=2 recently found from perturbative renormalisation group techniques, fulfill the correlation length bound \nu >= 2/d, and give further evidence against replica symmetry breaking in this class of models.