Star-graph expansions for bond-diluted Potts models

Details Star-graph expansions for bond-diluted Potts models Star-graph expansions for bond-diluted Potts models

2002-06-21

arxiv.org/abs/cond-mat/0206400v1

Phys. Rev. E67(2003)026118

Physics

Condensed Matter

Statistical Mechanics

8 pages, 6 figures

Scientific paper

10.1103/PhysRevE.67.026118

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 4-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 {\em et al.}, Phys. Rev. E64, 036120(2001)) shows signals for the softening to a second-order transition at finite disorder strength.

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