Thermodynamics of a spin-1 Bose gas with fixed magnetization

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.