FINITE-SIZE SCALING AND CRITICAL EXPONENTS - A NEW APPROACH AND ITS APPLICATION TO ANDERSON LOCALIZATION

Based on finite-size scaling ideas a new approach to analyse the singularities associated with second-order phase transitions is presented. Under certain requirements, the method allows to derive an upper limit for the critical exponent from finite-size data that describe the system far away from the transition. By extrapolation the critical exponent nu is determined. As an example, the approach is applied to the metal-insulator transition in disordered systems. The result nu = 1.35 +/- 0.15 is independent of the employed random distribution. With field theoretical arguments we discuss and generalize this result. Our results are consistent with the assumption that one-parameter scaling and universality are valid in the 3D Anderson model.