Hard hexagon partition function for complex fugacity

TL;DR

This paper investigates the complex analyticity of the hard hexagon model's partition function, revealing limitations of previous thermodynamic limit results and deriving a new algebraic equation for low density regimes.

Contribution

It provides a detailed analysis of the partition function's zeros and eigenvalues in the complex plane and introduces a novel algebraic equation for low density partition functions.

Findings

Partition function zeros indicate non-analyticity in the complex plane.

Baxter's thermodynamic limit does not fully capture complex analyticity.

A new algebraic equation for low density partition function is derived.

Abstract

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.