A mean field model for spin glasses based on a 2-level perceptron

We introduce a mean field model for spin glasses that is obtained by “iterating” the definition of the perceptron model of [SG] and we prove the validity of the replica-symmetric solution under a condition of the type “high temperature.” The replica-symmetric equations involve six different parameters. This model illustrates, on one hand, that we now have efficient tools to deal with such systems, and on the other hand, that it is probably unreasonable to hope for abstract theorems independent of the specific type of the system.