Competition between spin glass order and strong coupling superconductivity in a single-species fermion model

The phase diagram of a single species fermion model allowing for local pairing superconductivity (SC) and spin glass order (SG) is derived as a function of chemical potential \mu and ratio r=v/J between attractive coupling v and frustrated magnetic interaction J. For ratios larger than a characteristic r_c(\mu), superconductivity does not allow for SG order, while for smaller values a very detailed phase diagram arises with entangled spin glass and superconducting transitions. Our results for the Green's functions show that superconductivity occurring in the magnetic interaction band is of gapless type with a crossover from strongly gapless, within a certain range below T_c, to very weakly gapless in a wide low temperature regime, and hardgapped at T=0.