ANNEALED N-VECTOR P-SPIN MODEL

A disordered n-vector model with p spin interactions is introduced and studied in mean field theory for the annealed case. We present complete solutions for the cases n = 2 and n = 3, and have obtained explicit order parameter equations for all the stable solutions for arbitrary n. For all n and p we find one stable high-temperature phase and one stable low-temperature phase. The phase transition is of first order. For n = 2, it is continuous in the order parameters for p less-than-or-equal-to 4 and has a jump discontinuity in the order parameters if p > 4. For n = 3, it has a jump discontinuity in the order parameters for all p.