Star-graph expansions for bond-diluted Potts models

TL;DR

This paper develops high-temperature series expansions for bond-diluted Potts models, enabling analysis of phase transitions and disorder effects across various parameters, with results validated against Monte Carlo simulations.

Contribution

It introduces a star-graph expansion technique for exact quenched disorder averages in Potts models, allowing symbolic treatment of disorder strength and dimension.

Findings

Transition temperature decreases with increasing disorder p

Effective critical exponent γ varies with p, indicating transition softening

Results align with Monte Carlo data, showing transition change from first- to second-order

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 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.