QUENCHED N-VECTOR P-SPIN MODEL

A disordered n-vector model with p spin interactions previously introd uced is studied for the quenched case by means of the replica method a nd a generalized Parisi theory. We present formal solutions for genera l n and p and then study the case p --> infinity. The high-temperature solution is stable at all temperatures and there is only one phase tr ansition at a temperature T(g). Only longitudinal low-temperature solu tions are possible. There is one spin-glass solution, and it is stable for all T < T(g). The phase transition at T(g) is of first order and displays a jump discontinuity in the order parameters q(i)(L) and d Th e spin-glass free energy is temperature dependent for n > 1 while it i s constant when n = 1.