Star-graph expansions for bond-diluted Potts models.

Abstract

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 (p,d) 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.