Thermodynamics of a spin-1 Bose gas with fixed magnetization

TL;DR

This paper studies the thermodynamics of a spin-1 Bose gas with fixed magnetization, analyzing phase transitions and the effects of magnetic fields and interactions using grand canonical and classical fields methods.

Contribution

It provides a detailed analysis of phase transitions and the influence of magnetic fields and interactions on a spin-1 Bose gas with fixed magnetization, including analytical and numerical results.

Findings

Double phase transition due to global constraints.

Critical temperatures and condensate fractions are affected by magnetic fields.

Interactions influence the condensate scenario, especially below the second critical temperature.

Abstract

We investigate the thermodynamics of a spin-1 Bose gas with fixed magnetization including the quadratic Zeeman energy shift. Our calculations are based on the grand canonical description for the ideal gas and the classical fields approximation for atoms with ferromagnetic and antiferromagnetic interactions. We confirm the occurence of a double phase transition in the system that takes place due to two global constraints. We show analytically for the ideal gas how critical temperatures and condensed fractions are changed by a non-zero magnetic field. The interaction strongly affects the condensate scenario below the second critical temperature. The effect imposed by interaction energies becomes diminished in high magnetic fields where condensation, of both ferromagnetic and antiferromagnetic atoms, agree with the ideal gas results.