In the mean-field Bose gas at inverse temperature beta ~ N^{-2/3}, U(1) symmetry breaking occurs if and only if Bose-Einstein condensation occurs, with the quasi-average order parameter equal to the square root of the condensate fraction.
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A note on spontaneous symmetry breaking in the mean-field Bose gas
In the mean-field Bose gas at inverse temperature beta ~ N^{-2/3}, U(1) symmetry breaking occurs if and only if Bose-Einstein condensation occurs, with the quasi-average order parameter equal to the square root of the condensate fraction.