Locating Critical Points Using Ratios of Lee-Yang Zeros

TL;DR

This paper introduces a numerical method using ratios of Lee-Yang zeros and finite-size scaling to accurately locate critical points in systems, reducing finite-volume effects compared to traditional methods.

Contribution

The paper presents a novel approach leveraging Lee-Yang zeros ratios for critical point detection, improving accuracy over existing techniques like Binder-cumulant analysis.

Findings

Successfully locates the critical point in the 3D three-state Potts model with external field.

Demonstrates suppression of finite-volume effects compared to traditional methods.

Validates the method's effectiveness through numerical simulations.

Abstract

We propose a method to numerically determine the location of a critical point in general systems using the finite-size scaling of Lee-Yang zeros. This method makes use of the fact that the ratios of Lee-Yang zeros on various spatial volumes intersect at the critical point. While the method is similar to the Binder-cumulant analysis, it is advantageous in suppressing the finite-volume effects arising from the mixing of variables in general systems. We show that the method works successfully for numerically locating the CP in the three-dimensional three-state Potts model with a nonzero external field.