  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.
