Thermodynamics of the System of Massive Dirac Fermions in a Uniform Magnetic Field

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.

Automated summary

In this study, the grand partition function of a system of massive Dirac fermions in a uniform magnetic field was constructed from Landau levels, and thermodynamic quantities were obtained through an Abel-Plana formula. Expansion of these quantities in terms of the dimensionless variable b = 2eB/T (2) was carried out. Additionally, calculations of zero-field magnetic susceptibility, various currents, and energy-momentum tensor were performed, along with discussing mass correction effects on chiral separation. The study also showed the recovery of chiral magnetic effect and chiral separation effect for massless chiral fermions.