Density of Partition Function Zeroes and Phase Transition Strength

TL;DR

This paper introduces a novel numerical method to determine the density of partition function zeroes, enabling precise analysis of phase transition order and strength, and distinguishing between different types of transitions.

Contribution

The paper presents a new technique for extracting the density of partition function zeroes from finite lattice data, improving phase transition analysis.

Findings

Effective in distinguishing first and second order transitions

Applied successfully to various models using Fisher and Lee-Yang zeroes

Provides insights into finite-size scaling and transition crossover

Abstract

A new method to extract the density of partition function zeroes (a continuous function) from their distribution for finite lattices (a discrete data set) is presented. This allows direct determination of the order and strength of phase transitions numerically. Furthermore, it enables efficient distinguishing between first and second order transitions, elucidates crossover between them and illuminates the origins of finite-size scaling. The efficacy of the technique is demonstrated by its application to a number of models in the case of Fisher zeroes and to the XY model in the case of Lee-Yang zeroes.