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The momentum-shell renormalization group (RG) is used to study thecondensation of interacting Bose gases without and with disorder. First of all,for the homogeneous disorder-free Bose gas the interaction-induced shifts inthe critical temperature and chemical potential are determined up to secondorder in the scattering length. The approach does not make use of dimensionalreduction and is thus independent of previous derivations. Secondly, the RG isused together with the replica method to study the interacting Bose gas withdelta-correlated disorder. The flow equations are derived and found to reduce,in the high-temperature limit, to the RG equations of the classicalLandau-Ginzburg model with random-exchange defects. The random fixed point isused to calculate the condensation temperature under the combined influence ofparticle interactions and disorder.Comment: 7 pages, 2 figure

Condensation temperature of interacting Bose gases with and without disorder