Finite-size scaling of Lee-Yang zeros and its application to the 3-state Potts model and heavy-quark QCD

TL;DR

This paper introduces a new finite-size scaling method based on Lee-Yang zeros ratios to accurately identify critical points in statistical models and applies it to the Ising, Potts, and heavy-quark QCD models.

Contribution

The paper develops and validates a novel Lee-Yang zeros ratio method for locating critical points, applicable to various models including QCD.

Findings

The LYZR method accurately locates critical points in the Ising model.

The method successfully identifies the critical point in the 3-state Potts model.

It effectively determines the critical point in heavy-quark QCD simulations.

Abstract

We propose a new general method to study critical points (CP) using the finite-size scaling of Lee-Yang zeros (LYZ). We first study the LYZ in the three-dimensional Ising model on finite lattices. We show that the ratios of multiple LYZ (Lee-Yang-zero ratios: LYZR) have useful scaling properties similar to the Binder cumulants, providing us with a novel method to study CP. In numerical simulations of the Ising model, we confirm that this method works well. We then apply the method to analyze the CP in the three-dimensional three-state Potts model and finite-temperature QCD in heavy-quark region, which are believed to belong to the same universality class as the Ising model. In these models, the partition function at complex parameters can be evaluated by the reweighting method, which allows us to determine the LYZ by varying coupling parameters continuously around the CP. We demonstrate that the LYZR method is powerful in determining the location of the CP in these models.