Test of Guttmann and Enting's conjecture in the eight-vertex model

TL;DR

This paper examines the analyticity of the partition function series in the eight-vertex model, providing evidence supporting a conjecture about solvability in statistical mechanics through graphical techniques.

Contribution

It introduces a graphical method to analyze the series expansion and verifies a key aspect of Guttmann and Enting's conjecture.

Findings

Series terms have a pole at only one complex point

Supports the conjecture on model solvability

First terms of the series were explicitly obtained

Abstract

We investigate the analyticity property of the partially resummed series expansion(PRSE) of the partition function for the eight-vertex model. Developing a graphical technique, we have obtained a first few terms of the PRSE and found that these terms have a pole only at one point in the complex plane of the coupling constant. This result supports the conjecture proposed by Guttmann and Enting concerning the ``solvability'' in statistical mechanical lattice models.