Journal of Statistical Physics, Vol. 59, Nos. 3/4, 1990. p. 1077-1086.
Using a multi-spin coding algorithm, the Hopfield model is studied for network sizes up to N = 33,968. Thermodynamically stable states are found in a region where the replica-symmetric solution predicts none should exist, but where a one-step replica symmetry-breaking calculation predicts some should exist. Furthermore, the order parameter in this region is found to take on two distinct values, one of which is not predicted by any theory.