Discontinuous Phase Transitions in S-Paired Fermi Systems

The most general S-paired systems of fermions for which a gap equation can be separated according to the specific redefined variables, are considered. Moreover, a solution of this gap equation (gap energy) is obtained in a parametric form. It allows us to investigate thermodynamic properties of such systems i.e. the thermodynamic potential, entropy, heat capacity and critical magnetic induction. We show also that the heat capacity difference between the superconducting and the normal phase is entirely determined by the order parameter. The obtained results reveal possibilities of discontinuous phase transition to the normal state and moreover, the theorem on existence of such transitions is formulated and proved. The condition for the BCS-type energy gap is given, which additionally classifies properties of the heat capacity of S-paired phase by virtue of the shape of the energy gap. In order to illustrate the developed formalism, the numerical results for the so-called statistical spin liquids and application of the established methods to the experimental data conversion, are presented and discussed.