Random-bond Potts models on hypercubic lattices: high-temperature series expansions

We derive, high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices using a star-graph expansion technique. This method enables the exact calculation of quenched disorder averages for arbitrary uncorrelated coupling distributions. Moreover, we can keep the disorder strength p as well as the dimension d as symbolic parameters. This allows us to scan large regions of the (p, d) parameter space for any value of q. For the bond-diluted 4-state Potts model in three dimensions we present first results for the critical temperature as a function of p as obtained from the analysis of susceptibility series up to order 18.