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We present a new method for the numerical treatment of second order phasetransitions using the level spacing distribution function $P(s)$. We show thatthe quantities introduced originally for the shape analysis of eigenvectors canbe properly applied for the description of the eigenvalues as well. Theposition of the metal--insulator transition (MIT) of the three dimensionalAnderson model and the critical exponent are evaluated. The shape analysis of$P(s)$ obtained numerically shows that near the MIT $P(s)$ is clearly differentfrom both the Brody distribution and from Izrailev's formula, and the bestdescription 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.Comment: 14 pages in plain TeX, 6 figures upon reques

Shape analysis of the level-spacing distribution around the metal-insulator transition in the three-dimensional Anderson model