It is shown that an Ising spin system in which both spins and interactions evolve in time according to dynamical laws suggested by neural processes, but with widely separated timescales, leads to a thermodynamic equilibrium corresponding to a system of averaged replicas, where the replica number can take any real value determined by the ratio of characteristic temperatures. The resultant phase structure has interesting features which are explored.

• Received 9 August 1993

DOI:https://doi.org/10.1103/PhysRevB.48.16116