Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

Details Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model Shape Analysis of the Level Spacing Distribution around the Metal Insulator Transition in the Three Dimensional Anderson Model

1994-07-13

arxiv.org/abs/cond-mat/9407058v1

Physics

Condensed Matter

14 pages in plain TeX, 6 figures upon request

Scientific paper

10.1103/PhysRevB.52.7783

We present a new method for the numerical treatment of second order phase transitions using the level spacing distribution function $P(s)$. We show that the quantities introduced originally for the shape analysis of eigenvectors can be properly applied for the description of the eigenvalues as well. The position of the metal--insulator transition (MIT) of the three dimensional Anderson model and the critical exponent are evaluated. The shape analysis of $P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly different from both the Brody distribution and from Izrailev's formula, and the best description is of the form $P(s)=c_1\,s\exp(-c_2\,s^{1+\beta})$, with $\beta\approx 0.2$. This is in good agreement with recent analytical results.

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