Abstract
Three hyperfine states of Bose-condensed sodium atoms, recently optically trapped, can be described as a spin-1 Bose gas. We study the behaviour of this system in a magnetic field, and construct the phase diagram, where the temperature of the Bose condensation $T_{BEC}$ increases with magnetic field. In particular the system is ferromagnetic below $T_{BEC}$ and the magnetization is proportional to the condensate fraction in a vanishing magnetic field. Second derivatives of the magnetisation with regard to temperature or magnetic field are discontinuous along the phase boundary.
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