On the Phase Structure of QCD in a Finite Volume

TL;DR

This paper investigates how finite volume effects influence the curvature of the chiral phase transition line in QCD, using functional renormalization group methods with a quark-meson model, revealing significant boundary condition-dependent effects.

Contribution

It provides a detailed analysis of finite-volume impacts on QCD phase transition curvature, incorporating quark and meson fluctuations with boundary condition considerations.

Findings

Finite-volume effects significantly alter the transition curvature.

Periodic boundary conditions decrease the curvature in intermediate volumes.

Results suggest possible shifts in the QCD critical endpoint location.

Abstract

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.