We have examined the role of the BCS pairing mechanism in the formation of
the magnetic moment and henceforth a spin glass (SG) phase by studying a
fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the
fermions. This model is obtained by using perturbation theory to trace out the
conduction electrons degrees of freedom in conventional superconducting alloys.
The model is formulated in the path integral formalism where the spin operators
are represented by bilinear combinations of Grassmann fields and it reduces to
a single site problem that can be solved within the static approximation with a
replica symmetric Ansatz. We argue that this is a valid procedure for values of
temperature above the de Almeida-Thouless instability line. The phase diagram
in the T-g plane, where g is the strength of the pairing interaction, for fixed
variance J^2/N of the random couplings J_{ij}, exhibits three regions: a normal
paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase
where there is formation of local pairs.The NP and PAIR phases are separated by
a second order transition line g=g_{c}(T) that ends at a tricritical point
T_{3}=0.9807J, g_{3}=5,8843J, from where it becomes a first order transition
line that meets the line of second order transitions at T_{c}=0.9570J that
separates the NP and the SG phases. For T<T_{c} the SG phase is separated from
the PAIR phase by a line of first order transitions.
These results agree qualitatively with experimental data in
Gd_{x}Th_{1-x}RU_{2}.Comment: 26 pages, 5 figures, to appear in The European Physical Journal
