Renormalization-group analysis of the dilute Bose system in d dimensions 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 are 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 are obtained using a regular solution for the coupling constant which is obtained from the scaling equations. The relevance of the dilute Bose gas for recent experimental results is also discussed.