QCD equation of state at nonzero magnetic fields in the Hadron Resonance Gas model

Abstract

The Hadron Resonance Gas (HRG) model is considered to study the QCD equation of state for the case of nonzero external magnetic fields. Thermodynamic observables including the pressure, energy density, entropy density, magnetization and the speed of sound are presented as functions of the temperature and the magnetic field. The magnetization is determined to be positive, indicating that the hadronic phase of QCD is paramagnetic. The behavior of the speed of sound suggests that the deconfinement transition temperature is lowered as the magnetic field grows. Moreover, a simple correspondence is derived, which relates the magnetic catalysis of the quark condensate to the positivity of the beta-function in scalar QED.