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In the present paper we have analysed a fermionic infinite-ranged quantumHeisenberg spin glass (s=1/2) with a BCS coupling in real space in the presenceof an applied magnetic field. This model has been obtained by tracing out theconducting fermions in a superconducting alloy. The magnetic field is appliedin the resulting effective model. The problem is formulated in the pathintegral formalism where the spin variables are defined as bilinearcombinations of the Grassmann fields. The static approximation is used to treatboth the pairing and the spin terms together with the replica symmetry ansatz.Henceforth, the problem can be reduced to a one site problem. The field in thez direction, Hz, separates the order parameters in two groups: parallel andtransverse to it. We have obtained a phase diagram in T-g space with zerotransverse spin-glass ordering, g being the strength of the pairinginteraction. It has been possible to locate the transition temperature betweenthe normal paramagnetic phase (NP) and the phase where there is a long rangeorder corresponding to formation of pairs (PAIR). The transition ends at thetemperature Tf, the transition temperature between the NP phase and the spinglass (SG) phase. Tf decreases for stronger fields allowing us to calculate theNP-PAIR line transition even at low temperatures. The NP-PAIR transition linehas a complex dependence with g and Hz, having a tricritical point depending onHz from where second order transitions occur for higher values of g and firstorder transitions occur for lower values of g.Comment: Accepted for publication in Phys. Rev.

Fermionic Heisenberg model for spin glasses with BCS pairing interaction