A perturbative expansion for the Hopfield model

We construct a perturbative series for order parameters and other interesting observables of the Hopfield model. It is shown that the L(2) norm of the n-th term of the expansion is bounded by alpha(n). We apply this construction to the L(2) fluctuation of the order parameter r and we find that the coefficients of its expansion vanish in the thermodynamic limit. Using a recent result [1] we deduce that the replica symmetric solution of the Hopfield model holds at any order of alpha.