QCD Thermodynamics and Neutral Pion in a Uniform Magnetic Field: Finite Volume Effects

TL;DR

This paper investigates finite volume effects in lattice QCD calculations under magnetic fields, focusing on thermodynamic quantities and neutral pion behavior, revealing volume-dependent corrections and invariances useful for accurate simulations.

Contribution

It provides a detailed analysis of finite volume effects on QCD thermodynamics and neutral pion properties in magnetic fields using chiral perturbation theory.

Findings

Volume and source averaging exploit magnetic periodicity.

Certain observables are volume-independent in specific directions.

Finite volume corrections significantly affect magnetic polarizability and pressure anisotropy.

Abstract

We address finite volume effects of lattice QCD calculations in background magnetic fields. Using chiral perturbation theory at next-to-leading order, volume effects are calculated for thermodynamic quantities: the chiral condensate, pressure anisotropy, and magnetization. The neutral pion effective action in a finite volume is additionally derived. For these charge neutral observables, volume and source averaging are shown to capitalize on magnetic periodicity, which is the remnant translational invariance of the finite-volume theory. For a fixed magnetic field strength, certain volume and source averaged quantities are independent of the size of the lattice transverse to the magnetic field. Despite this simplifying feature, finite volume corrections to the magnetic field dependence of the chiral condensate and neutral pion magnetic polarizability can be non-negligible. The pressure anisotropy at fixed magnetic flux, moreover, appears acutely sensitive to the lattice volume.