Renormalization-group approach to a Bose system. II. Condensed phase

The critical behavior in the condensed phase of a Bose system is studied by the renormalization-group method using Bogolubov's well-known prescription for eliminating the condensate operators. Scaling relations and an equation of state in the Griffiths form are derived with explicit expressions for the critical exponents and the scaling function up to first order in $\epsilon =4-d$. The results strengthen the conclusion reached in an earlier paper, namely, that critical behavior in a given symmetry class is independent of the classical or quantum nature of a phase transition.