Searching for Yang-Lee zeros in O($N$) models

TL;DR

This paper investigates the Lee-Yang zeros in O(N) models near phase transitions, aiming to locate the critical point using complex Langevin simulations to understand thermodynamic singularities.

Contribution

It introduces a novel approach to locate Lee-Yang edge singularities in O(N) models through complex Langevin methods, advancing understanding of phase transition phenomena.

Findings

Identification of the Lee-Yang edge singularity location

Application of complex Langevin simulations to O(N) models

Insights into the thermodynamics near critical points

Abstract

Near the second order phase transition point, QCD with two flavours of massless quarks can be approximated by an O($4$) model, where a symmetry breaking external field $H$ can be added to play the role of quark mass. The Lee-Yang theorem states that the equation of state in this model has a branch cut along the imaginary $H$ axis for $|Im[H]|>H_c$, where $H_c$ indicates a second order critical point. This point, known as Lee-Yang edge singularity, is of importance to the thermodynamics of the system. We report here on ongoing work to determine the location of $H_c$ via complex Langevin simulations.