Renormalization - group analysis of dilute Bose system in d - dimension at finite temperature

We study the d - dimensional Bose gas at finite temperature using the renormalization group method. The flow - equations and the free energy have been obtained for dimension d, and the cases d<2 and d=2 have been analysed in the limit of low and high temperatures. The critical temperature, the coherence length and the specific heat of a two dimensional Bose gas have been obtained using a solution for the coupling constant which does not present a singular behavior.