Crossover from diffusive to strongly localized regime in two-dimensional systems

We have studied the conductance distribution function of two-dimensional disordered noninteracting systems in the crossover regime between the diffusive and the localized phases. The distribution is entirely determined by the mean conductance, >, in agreement with the strong version of the single-parameter scaling hypothesis. The distribution seems to change drastically at a critical value very close to one. For conductances larger than this critical value, the distribution is roughly Gaussian while for smaller values it resembles a log-normal distribution. The two distributions match at the critical point with an often appreciable change in behavior. This matching implies a jump in the first derivative of the distribution which does not seem to disappear as system size increases. We have also studied 1/> corrections to the skewness to quantify the deviation of the distribution from a Gaussian function in the diffusive regime.