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.