A new approach to localization

Abstract

Attention is drawn to theorems on the convergence of random series. The theorems are applied to the Anderson transition for extended states and give good results for the critical ratio and the results are confirmed by the memory function method. It is predicted that the electronic specific heat at an Anderson transition should have a singularity and the ratio of it to the minimum metallic conductivity is found to be proportional to the temperature via a universal constant. The random series method suggests that it is incorrect to average Z or log Z to derive the singular behaviour of the specific heat or susceptibility in spin glasses. The specific heat per spin of spin glasses at the transition is found universally to be k per spin. The random series method gives the upper critical dimension of spin glasses and electronic random systems to be eight.