Thermodynamics of Chiral Fermion System in a Uniform Magnetic Field

We construct the grand partition function of the system of chiral fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Taking use of Abel-Plana formula, these thermodynamic quantities can be expanded as series with respect to a dimensionless variable $b=2eB\mathrm{/}{T}^2$. We find that the series expansions of energy density, pressure, magnetization intensity and magnetic susceptibility contain a singular term with $\ln b^2$, while particle number density, entropy density and heat capacity are power series of $b^2$. The asymptotic behaviors of these thermodynamic quantities in extreme conditions are also discussed.