Replica field theory for composite media

In this paper we use the replica trick together with a variational method in order to compute the effective permittivity of a medium where the local permittivity is a random binary variable. We obtain an effective-medium formula previously derived by a cumulant expansion. This formula is satisfactory from many points of view (Hashin and Shtrikman bounds, low density expansion, etc.) showing that the replica method does not violate some basic principles.