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 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.

8 pages, 6 figures

References in corpus (1)

• A library of extended high-temperature expansions of basic observables for the spin S Ising models on two- and three-dimensional lattices

Cited by in corpus (7)

• Monte Carlo Study of Phase Transitions in the Bond-Diluted 3D 4-State Potts Model
• The Harris-Luck criterion for random lattices
• High-temperature series expansions for the $q$-state Potts model on a hypercubic lattice and critical properties of percolation
• High-temperature series for the bond-diluted Ising model in 3, 4 and 5 dimensions
• Approximate ground states of the random-field Potts model from graph cuts
• Geometrical Phase Transitions
• The SU(3) spin model with chemical potential by series expansion techniques