Fat and Thin Fisher Zeroes

TL;DR

This paper develops methods to determine the distribution of Fisher zeroes in the thermodynamic limit for Ising models on different types of random graphs, revealing insights into phase transitions.

Contribution

It introduces a unified approach to find Fisher zeroes for Ising models on planar and mean-field random graphs using free energy branch matching.

Findings

Fisher zeroes can be located by matching real parts of free energy branches.

Series expansions are straightforward for random graph Ising models.

Methods apply to both planar and mean-field graph models.

Abstract

We show that it is possible to determine the locus of Fisher zeroes in the thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs and their dual quadrangulations by matching up the real part of the high- and low-temperature branches of the expression for the free energy. Similar methods work for the mean-field model on generic, ``thin'' graphs. Series expansions are very easy to obtain for such random graph Ising models.