Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

TL;DR

This paper introduces a method linking energy level statistics and phase transitions, applying it to the Anderson model to determine critical parameters of the metal-insulator transition.

Contribution

It presents a novel approach using finite-size scaling of energy level statistics to analyze second-order phase transitions, specifically applied to the Anderson localization model.

Findings

Critical disorder W_c=16.5

Critical exponent ν=1.34

Effective description of metal-insulator transition

Abstract

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $\nu=1.34$ are computed.