Journal of Statistical Physics, Vol. 110, Nos. 1/2, January 2003. p. 51-72.
In this note, we prove a quenched large deviation result for the overlap of a p-spins interaction system at high temperature. The rate function of the large deviation principle is proved to be deterministic, and some of its basic properties are studied. Our result is based on a pure state result for a multidimensional p-spins system combined with a careful application of the Gärtner–Ellis Theorem.