We discuss a detailed phase diagram and other microscopic characteristics on the applied magnetic field - temperature (H_a-T) plane for a simple model of correlated fluid represented by a two-dimensional (2D) gas of heavy quasiparticles with masses dependent on the spin direction and the effective field generated by the electron correlations. The consecutive transitions between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases are either continuous or discontinuous, depending on the values of H_a and T. In the latter case, weak metamagnetic transitions occur at the BCS-FFLO boundary. We single out two different FFLO phases, as well as a reentrant behaviour of one of them at high fields. The results are compared with those for ordinary Landau quasiparticles in order to demonstrate the robustness of the FFLO states against the BCS state for the case with spin-dependent masses (SDM). We believe that the mechanism of FFLO stabilization by SDM is generic: other high-field low-temperature (HFLT) superconducting phases benefit from SDM as well.
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