Finite size effect on the thermodynamics of a hot and magnetized hadron resonance gas

Abstract: The thermodynamic properties of a non-interacting ideal Hadron Resonance Gas (HRG) of finite volume have been studied in the presence of an external magnetic field. The inclusion of background magnetic field in the calculation of thermodynamic potential is done by the modification of the dispersion relations of the charged hadrons in terms of Landau quantization. The generalized Matsubara prescription has been employed to take into account the finite size effects in which a periodic (anti-periodic) boundary conditions is considered for the mesons (baryons). We find significant effects of the magnetic field as well as system size on the temperature dependence of energy density, longitudinal and transverse pressure especially in low temperature regions. The HRG is found to exhibit diamagnetism (paramagnetism) in the low (high) temperature region whereas the finite size effect is seen to strengthen the diamagnetic behavior of the medium.