  This paper is devoted to a detailed study of a p-spins interaction model with
external field, including some sharp bounds on the speed of self averaging of
the overlap as well as a central limit theorem for its fluctuations, the
thermodynamical limit for the free energy and the definition of an
Almeida-Thouless type line. Those results show that the external field
dominates the tendency to disorder induced by the increasing level of
interaction between spins, and our system will share many of its features with
the SK model, which is certainly not the case when the external magnetic field
vanishes.
