P. A. Lee

Scaling studies of localization

Abstract The Anderson model of localization in two dimensions is studied using a numerical implementation of the real space sacling method. We conclude that extended states exist with a minimum metallic conductivity of ≈0.13 e 2 / n . These results are compared with the theory of Abrahams, Anderson, Licciardello and Ramakrishnan. Extension of their work to include spin flip scattering shows that the logarithmic divergence they find is cut-off at least in this case.

Magnetic Susceptibility at a Peierls Transition

The effects of fluctuations on the Peierls transition in one dimension are calculated by taking a functional average over variations in the order parameter. It is found that the transition is suppressed to a temperature of approximately one quarter of the mean‐field transition but remains fairly sharp. The density of states which determines the Pauli susceptibility is found to decrease in the temperature interval between one half and one quarter of the mean field transition temperature. The effects of fluctuations on other properties are discussed and a brief comparison made to experimental systems. A more complete description of this work has been given elsewhere.(1)