HALL-EFFECT IN COMPOSITE MEDIA - A REPLICA APPROACH

In this letter we use the replica trick together with a variational me thod in order to compute the effective conductivity tensor of a disord ered binary composite in a static magnetic field. When only one of the two components percolates, the effective magnetoresistivity rho(xx)(e ) saturates for strong magnetic fields h as in a homogeneous material. When both components percolate, the effective magnetoresistivity disp lays an anomalous behaviour and scales like the magnetic field h. At t he percolation threshold of one component (denoted by p(c)), the scali ng exponent nu (rho(xx)(e) approximately h(nu)) is equal to 2/3 and th ere is a scaling behaviour with both h and p - p(c) (where p denotes t he volume fraction). This indicates that there is a field-dependent co rrelation length at strong fields that is distinct from the percolatio n correlation length. In all cases the effective Hall constant R(H) sa turates at strong fields.