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.