A PERTURBATIVE EXPANSION FOR THE HOPFIELD MODEL

We construct a perturbative series for order parameters and other inte resting observables of the Hopfield model. It is shown that the L(2) n orm 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 an d we find that the coefficients of its expansion vanish in the thermod ynamic limit. Using a recent result [1] we deduce that the replica sym metric solution of the Hopfield model holds at any order of alpha.