We present a no fitting method for the numerical treatment of second-order phase transitions using the level-spacing distribution function P(s). The position of the metal-insulator transition (MIT) of the three-dimensional Anderson model and the critical exponent are evaluated (${\mathit{W}}_{\mathit{c}}$≊16.75, ν≊1.3). The shape analysis of P(s) shows that near the MIT it is clearly different from both the Brody distribution and from Izrailev’s formula, and the best description is of the form P(s)=${\mathit{c}}_1$s exp(-${\mathit{c}}_2$${\mathit{s}}^{1+\gamma }$), with γ≊0.2. This is in good agreement with recent analytical results. At the same time our results provide the numerical confirmation of the relation between γ and the critical exponent ν, γ=1/dν.

• Received 2 June 1995

DOI:https://doi.org/10.1103/PhysRevB.52.7783