Thermodynamics and response to a weak magnetic field in a model of superconductivity in a singular Fermi liquid

Model of a superconducting singular Fermi liquid with divergent scattering amplitude for particles with the same momenta is considered within the Bogolubov method. The system displays a pseudogap behavior and the phase transition between the superconducting and the normal phase is found to be of the first order with a pronounced discontinuity in the entropy. The response of the system to a weak magnetic field acting on both spin and charge degrees of freedom is studied. The spin susceptibility and the magnetic field penetration depth are discussed. Numerical results for the s-wave paired singular Fermi liquid are presented.