O(2)-scaling in finite and infinite volume

TL;DR

This paper investigates the universality class of the chiral phase transition in QCD using finite-size scaling analysis and functional renormalization group methods to distinguish between O(2) and O(4) behaviors.

Contribution

It introduces a new finite-size scaling analysis using the functional renormalization group to clarify the universality class of the QCD chiral phase transition.

Findings

Finite-size scaling analysis favors the O(2) universality class.

Binder cumulant analysis supports the O(2) behavior.

Provides a methodological framework for analyzing critical fluctuations in lattice QCD.

Abstract

The exact nature of the chiral phase transition in QCD is still under investigation. In $N_f=2$ and $N_f=(2+1)$ lattice simulations with staggered fermions the expected O($N$)-scaling behavior was observed. However, it is still not clear whether this behavior falls into the O(2) or O(4) universality class. To resolve this issue, a careful scaling and finite-size scaling analysis of the lattice results is needed. We use a functional renormalization group to perform a new investigation of the finite-size scaling regions in O(2)- and O(4)-models. We also investigate the behavior of the critical fluctuations by means of the $4^{\text{th}}$-order Binder cumulant. The finite-size analysis of this quantity provides an additional way for determining the universality class of the chiral phase transition in lattice QCD.