  In this article, we propose a new method to compute the effective properties
of non-linear disordered media. We use the fact that the effective constants
can be defined through the minimum of an energy functional. We express this
minimum in terms of a path integral allowing us to use many-body techniques. We
obtain the perturbation expansion of the effective constants to second order in
disorder, for any kind of non-linearity. We apply our method to both cases of
strong and weak non-linearities. Our results are in agreement with previous
ones, and could be easily extended to other types of non-linear problems in
disordered systems.
