Journal of Statistical Physics, Vol. 45, Nos. 1/2, 1986. p. 99-112.
The spherical-model limit n -> oo of the n-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which the n -> oo and replica limits limits are interchanged, provided the replica
and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained...