Fermionic Heisenberg model for spin glasses with BCS pairing interaction

In the present paper we have analyzed a fermionic infinite-ranged quantum H eisenberg spin glass (s = 1/2) with a BCS coupling in real space in the pre sence of an applied magnetic field. This model has been obtained by tracing out the conducting fermions in a superconducting alloy. The magnetic field is applied in the resulting effective model. The problem is formulated in the path integral formalism where the spin variables are defined as bilinea r combinations of the Grassmann fields. The static approximation is used to treat both the pairing and the spin terms together with the replica symmet ry ansatz. Henceforth, the problem can be reduced to a one site problem. Th e field in the z direction, H-z, separates the order parameters in two grou ps: parallel and transverse to it. We have obtained a phase diagram in T-g space with zero transverse spin-glass ordering, g being the strength of the pairing interaction. It has been possible to locate the transition tempera ture between the normal paramagnetic phase (NP) and the phase where there i s a long range order corresponding to formation of pairs (PAIR). The transi tion ends at the temperature T-f, the transition temperature between the NP phase and the spin glass (SG) phase. T-f decreases for stronger fields all owing us to calculate the NP-PAIR line transition even at low temperatures. The NP-PAIR transition line has a complex dependence with g and H-z, havin g a tricritical point depending on H-z from where second order transitions occur for higher values of g and first order transitions occur for lower va lues of g.