High-Temperature Series Expansions for Random Potts Models

TL;DR

This paper develops high-temperature series expansions for the free energy and susceptibility of random-bond q-state Potts models on hypercubic lattices, enabling exact disorder averaging for various coupling distributions.

Contribution

It introduces a star-graph expansion technique that allows exact quenched disorder averages with symbolic parameters for the first time.

Findings

Series analysis for 3D Ising model susceptibility up to order 19.

Comparison with field-theoretical and Monte Carlo results.

Enhanced understanding of disorder effects in Potts models.

Abstract

We discuss recently generated high-temperature series expansions for the free energy and the susceptibility of random-bond q-state Potts models on hypercubic lattices. Using the star-graph expansion technique quenched disorder averages can be calculated exactly for arbitrary uncorrelated coupling distributions while keeping the disorder strength p as well as the dimension d as symbolic parameters. We present analyses of the new series for the susceptibility of the Ising (q=2) and 4-state Potts model in three dimensions up to order 19 and 18, respectively, and compare our findings with results from field-theoretical renormalization group studies and Monte Carlo simulations.