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 of the two components percolates, the effective magnetoresistivity ρ_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 ν (ρ_xx^(e)∼h^ν) 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.