Star-graph expansions for bond-diluted Potts models

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. By applying several series analysis techniques to the new series expansions, one can scan large regions of the $\mathrm{}(p,d)\mathrm{}$ parameter space for any value of q. For the bond-diluted four-state Potts model in three dimensions, which exhibits a rather strong first-order phase transition in the undiluted case, we present results for the transition temperature and the effective critical exponent $\gamma$ as a function of p as obtained from the analysis of susceptibility series up to order 18. A comparison with recent Monte Carlo data [Chatelain et al., Phys. Rev. E 64, 036120 (2001)] shows signals for the softening to a second-order transition at finite disorder strength.