Journal of Statistical Physics, Vol. 68, Nos. 5/6, 1992. p. 925-976.
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 = 4 or less 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.