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Cold asymmetrical fermion superfluids in nonperturbative renormalisation group

The application of the nonperturbative renormalisation group approach to a system with two fermion species is studied. Assuming a simple ansatz for the effective action with effective bosons, describing pairing effects we derive a set of approximate flow equations for the effective coupling including boson and fermionic fluctuations. The case of two fermions with different masses but coinciding Fermi surfaces is considered. The phase transition to a phase with broken symmetry is found at a critical value of the running scale. The large mass difference is found to disfavour the formation of pairs. The mean-field results are recovered if the effects of boson loops are omitted. While the boson fluctuation effects were found to be negligible for large values of $p_{F} a$ they become increasingly important with decreasing $p_{F} a$ thus making the mean field description less accurate.