The QCD equation of state in background magnetic fields

TL;DR

This study computes the QCD equation of state under magnetic fields using a novel lattice method, revealing paramagnetic behavior and a reduced transition temperature in the presence of magnetic fields.

Contribution

A new lattice-based method for determining the QCD free energy at nonzero magnetic fields, enabling analysis up to large magnetic field strengths.

Findings

Transition temperature decreases with magnetic field.

QCD medium is paramagnetic around and above transition temperature.

Evidence of weak diamagnetism at low temperatures.

Abstract

We determine the equation of state of 2+1-flavor QCD with physical quark masses, in the presence of a constant (electro)magnetic background field on the lattice. To determine the free energy at nonzero magnetic fields we develop a new method, which is based on an integral over the quark masses up to asymptotically large values where the effect of the magnetic field can be neglected. The method is compared to other approaches in the literature and found to be advantageous for the determination of the equation of state up to large magnetic fields. Thermodynamic observables including the longitudinal and transverse pressure, magnetization, energy density, entropy density and interaction measure are presented for a wide range of temperatures and magnetic fields, and provided in ancillary files. The behavior of these observables confirms our previous result that the transition temperature is reduced by the magnetic field. We calculate the magnetic susceptibility and permeability, verifying that the thermal QCD medium is paramagnetic around and above the transition temperature, while we also find evidence for weak diamagnetism at low temperatures.