  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.
