Thermodynamics of Chiral Fermion System in a Uniform Magnetic Field

TL;DR

This paper derives the thermodynamic properties of chiral fermions in a magnetic field using Landau levels and series expansions, revealing singular and power-law behaviors in various quantities.

Contribution

It introduces a method to compute thermodynamic quantities of chiral fermions in magnetic fields via Landau levels and series expansions, highlighting singular terms.

Findings

Series expansions contain a logarithmic singularity in magnetic field strength.

Energy density, pressure, magnetization, and susceptibility show logarithmic divergence.

Particle density, entropy, and heat capacity follow power series in magnetic field.

Abstract

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 $b=2eB/T^{2}$. 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.