The metal--insulator transition in disordered systems: a new approach to the critical behaviour

In the most popular approach to the numerical study of the Anderson metal-insulator transition the transfer matrix method is combined with finite-size scaling ideas. This approach requires large computer resources to overcome the statistical fluctuations and to accumulate data for a sufficient range of different values of disorder or energy. In this paper we present an alternative approach in which the basic transfer matrix is extended to calculate the derivative with respect to disorder. By so doing we are able to concentrate on a single value of energy or disorder and, potentially, to calculate the critical behaviour much more efficiently and independently of the assumed range of the critical regime. We present some initial results which illustrate both the advantages and the drawbacks of the method.