  We derive a field-theoretical representation for the moments of the
eigenstates in the generalized Anderson model. The representation is exact and
can be used for the Anderson model with generic non-random hopping elements in
any dimensions. We apply this method to the simplex model, for which the
hopping amplitude between any two lattice sites is the same, and find that the
eigenstates are localized at any strength of disorder. Our analytical
predictions are in excellent agreement with the results of numerical
simulations.
