Low Temperature Expansions for Potts Models

TL;DR

This paper develops low temperature series expansions for the three-state and eight-state Potts models on simple cubic lattices, providing detailed calculations of energy, magnetization, and susceptibility.

Contribution

It introduces a recursive enumeration method for low temperature series expansions of Potts models in two and three dimensions, extending previous computational techniques.

Findings

Series expansions up to 45 excited bonds for 3-state Potts in 2D

Series expansions up to 39 excited bonds for 3-state Potts in 3D

Series expansions up to 25 excited bonds for 8-state Potts in 2D

Abstract

On simple cubic lattices, we compute low temperature series expansions for the energy, magnetization and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds respectively, and the eight-state Potts model in D=2 to 25 excited bonds. We use a recursive procedure which enumerates states explicitly. We analyze the series using Dlog Pade analysis and inhomogeneous differential approximants.