Journal of Statistical Physics, Vol. 71, Nos. 3/4, 1993, p. 361-378.
The probability distributions for the overlaps between and the self-correlations of the pure states of the Stanley n-vector model with infinite-range interactions are derived. These probability distributions represent two new order parameters for the model and are intimately related to the parameters which arise naturally within the replica formalism for the treatment of the corresponding quenched random-bond model. In contrast to the n = 1 Ising case, the probability distributions are nontrivial when n > 1 and an additional parameter for self-correlation has to be introduced.