Critical endpoint of QCD in a finite volume

TL;DR

This paper examines how finite volume effects influence the position of the critical endpoint in the QCD phase diagram using lattice Yang--Mills theory and Dyson--Schwinger equations, finding minimal effects for volumes larger than 8 fm.

Contribution

It provides a detailed analysis of finite volume impacts on the QCD critical endpoint using a combined lattice and Dyson--Schwinger approach, extending understanding beyond infinite-volume assumptions.

Findings

Volume effects are significant only for L ≤ 5 fm.

Volumes larger than 8 fm are close to infinite-volume results.

The critical endpoint's location is sensitive to boundary conditions at small volumes.

Abstract

We investigate the impact of finite volume and the corresponding restrictions on long-range correlations on the location of the critical endpoint in the QCD phase diagram. To this end, we employ a sophisticated combination of lattice Yang--Mills theory and a (truncated) version of Dyson--Schwinger equations in Landau gauge for $2 + 1$ quark flavors that has been studied extensively in the past. In the infinite-volume limit, this system predicts a critical endpoint at moderate temperature and large chemical potential. We study this system at small and intermediate volumes and determine the dependence of the location of the critical endpoint on the boundary conditions and the volume of a three-dimensional cube with edge length $L$. We demonstrate that noticeable volume effects of more than five percent only occur for $L \lesssim 5 \, \text{fm}$ and that volumes as large as $L^3 \gtrsim (8 \, \text{fm})^3$ are very close to the infinite-volume limit.