Thermodynamics of the system of massive Dirac fermions in a uniform magnetic field

Abstract

We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel-Plana formula, these thermodynamic quantities can be expanded as power series with respect to the dimensionless variable $b=2eB/T^{2}$. The zero-field magnetic susceptibility is expanded at zero mass, and the leading order term is logarithmic. We also calculate scalar, vector current, axial vector current and energy-momentum tensor of the system through ensemble average approach. Mass correction to chiral separation effect is discussed. For massless chiral fermions, our results recover the chiral magnetic effect for right- and left-handed fermions, as well as chiral separation effect.