Phase transition strengths from the density of partition function zeroes

TL;DR

This paper introduces a novel numerical method to analyze phase transitions by examining the density of partition function zeroes, aiding in distinguishing transition types and understanding finite-size effects.

Contribution

The paper presents a new approach to determine phase transition order and strength directly from zeroes density, improving analysis of finite-size systems.

Findings

Effective in identifying first- and second-order transitions

Clarifies the crossover between different transition types

Provides insights into finite-size scaling origins

Abstract

We report on a new method to extract thermodynamic properties from the density of partition function zeroes on finite lattices. 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 power of the method is illustrated in typical applications for both Fisher and Lee-Yang zeroes.