Numerical Study of the Roberge-Weiss Transition

TL;DR

This paper numerically investigates the Roberge-Weiss phase transition in lattice QCD, analyzing Lee-Yang zeros and quark density discontinuities to understand the transition at finite temperature and density.

Contribution

It introduces a polynomial fit approach to analyze lattice QCD data and links Lee-Yang zeros to the Roberge-Weiss transition, providing new insights into phase transition analysis.

Findings

Lee-Yang zeros lie on the negative real axis at high temperature

Lee-Yang zeros' density matches the quark density discontinuity

The polynomial fit method effectively analyzes finite density lattice QCD data

Abstract

We study the Roberge-Weiss phase transition numerically. The phase transition is associated with the discontinuities in the quark-number density at specific values of imaginary quark chemical potential. We parameterize the quark number density $\rho_q$ by the polynomial fit function to compute the canonical partition functions. We demonstrate that this approach provides a good framework for analyzing lattice QCD data at finite density and a high temperature. We show numerically that at high temperature, the Lee-Yang zeros lie on the negative real semi-axis provided that the high-quark-number contributions to the grand canonical partition function are taken into account. These Lee-Yang zeros have nonzero linear density, which signals the Roberge-Weiss phase transition. We demonstrate that this density agrees with the quark density discontinuity at the transition line.