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A homogeneous Bose gas is investigated at finite temperature usingrenormalization group techniques. A non--perturbative flow equation for theeffective potential is derived using sharp and smooth cutoff functions.Numerical solutions of these equations show that the system undergoes a secondorder phase transition in accordance with universality arguments. We obtain thecritical exponent $\nu =0.73$ to leading order in the derivative expansion.Comment: 20 pages, 6 Postscript figures, revte

Application of renormalization-group techniques to a homogeneous Bose gas at finite temperature