Finite temperature phase diagram of a spin-1 Bose gas
  We formulate a self-consistent Hartree-Fock theory for a spin-1 Bose gas at finite temperature and apply it to characterizing the phase diagram. We find that spin coherence between thermal atoms in different magnetic sub-levels develops via coherent collisions with the condensed atoms, and is a crucial factor in determining the phase diagram. We develop analytical expressions to characterize the interaction and temperature dependent shifts of the phase boundaries. 
Yuki Kawaguchi, Nguyen Thanh Phuc, and P. Blair Blakie
cond-mat.quant-gas