One-loop omega-potential of charged massive particles in a constant homogeneous magnetic field at high temperatures

TL;DR

This paper derives high-temperature expansions for the one-loop omega-potential of charged particles in a magnetic field, analyzing phase transitions and thermodynamic properties, including effects of ring diagram summation.

Contribution

It provides explicit formulas for high-temperature corrections and non-perturbative effects, revealing phase transition behaviors in charged scalar gases under magnetic fields.

Findings

First-order phase transition from diamagnetic to superconducting state at high densities.

Inclusion of ring diagrams alters the phase to ferromagnetic at high densities and low temperatures.

Explicit high-temperature expansion formulas for omega-potential and effective action.

Abstract

The explicit expressions for the high-temperature expansions of the one-loop corrections to the omega-potential coming from charged scalar and Dirac particles and, separately, from antiparticles in a constant homogeneous magnetic field are derived. The explicit expressions for the non-perturbative corrections to the effective action at finite temperature and density are obtained. Thermodynamic properties of a gas of charged scalars in a constant homogeneous magnetic field are analyzed in the one-loop approximation. It turns out that, in this approximation, the system suffers a first-order phase transition from the diamagnetic to the superconducting state at sufficiently high densities. The improvement of the one-loop result by summing the ring diagrams is investigated. This improvement leads to a drastic change in thermodynamic properties of the system. The gas of charged scalars passes to the ferromagnetic state in place of the superconducting one at high densities and sufficiently low temperatures, in the high temperature regime.