QCD thermodynamics and neutral pion in a uniform magnetic field: Finite volume effects

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 in the chiral regime.

Automated summary

We investigate the effects of finite volume in lattice QCD calculations with background magnetic fields. By employing chiral perturbation theory at next-to-leading order, we calculate the volume effects on thermodynamic quantities, including the chiral condensate, pressure anisotropy, and magnetization. Additionally, we derive the effective action for neutral pions in a finite volume. For charge neutral observables, volume and source averaging take advantage of magnetic periodicity, which is the remaining translational invariance of the theory in finite volume. While certain volume and source averaged quantities remain independent of the lattice size perpendicular to the magnetic field, finite volume corrections to the chiral condensate and neutral pion magnetic polarizability can still be significant. Moreover, the pressure anisotropy at fixed magnetic flux is highly sensitive to the lattice volume in the chiral regime.