Replica field theory for composite media

M. Barthélémy; H. Orland

doi:doi:10.1051/jp1:1993239

DOI: 10.1051/jp1:1993239
J. Phys. I France 3 (1993) 2171-2177

Replica field theory for composite media

M. Barthélémy¹ and H. Orland²

¹ CEA-Centre d'études de Limeil-Valenton, Service Théorie et Etudes Nouvelles, 94195 Villeneuve-St-Georges Cedex, France
² CEA-Centre d'études de Saclay, Service de Physique Théorique, 91191 Gif-sur-Yvette Cedex, France

(Received 28 June 1993, accepted 21 July 1993)

Abstract
In this paper, we use the replica trick in order to compute the effective permittivity of a medium where the local permittivity is a random binary variable. A Gaussian variational treatment leads us to self-consistent equations which are solved and yield a replica diagonal solution (no replica symmetry breaking). We obtain an effective-medium formula previously derived by a cumulant expansion. This formula is satisfactory from many points of views (Hashin and Shtrikman bounds, low density expansion, etc) showing that the replica method does not violate some basic principles.