HALL-EFFECT IN COMPOSITE MEDIA - A REPLICA APPROACH

In this letter we use the replica trick together with a variational method in order to compute the effective conductivity tensor of a disordered 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 displays an anomalous behaviour and scales like the magnetic field h. At the percolation threshold of one component (denoted by p(c)), the scaling exponent nu (rho(xx)(e) approximately h(nu)) is equal to 2/3 and there is a scaling behaviour with both h and p - p(c) (where p denotes the volume fraction). This indicates that there is a field-dependent correlation length at strong fields that is distinct from the percolation correlation length. In all cases the effective Hall constant R(H) saturates at strong fields.