REPLICA FIELD-THEORY FOR COMPOSITE MEDIA

In this paper, we use the replica trick in order to compute the effect ive permittivity of a medium where the local permittivity is a random binary variable. A Gaussian variational treatment leads us to self-con sistent equations which are solved and yield a replica diagonal soluti on (no replica symmetry breaking). We obtain an effective-medium formu la previously derived by a cumulant expansion. This formula is satisfa ctory from many points of views (Hashin and Shtrikman bounds, low dens ity expansion, etc) showing that the replica method does not violate s ome basic principles.