Functional renormalisation group approach is applied to a imbalanced many- fermion system with a short-range attractive force. Composite boson field is introduced to describe the pairing between different flavour fermions. A set of approximate flow equations for the effective couplings is derived and solved. We identify the critical values of mass and particle number density mismatch when the system undergoes a phase transition to a normal state and determine the phase diagram both at unitary regime and nearby.
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