Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition

The nearest-neighbor level spacing distribution is numerically investigated by directly diagonalizing disordered Anderson Hamiltonians for systems of sizes up to $100\times 100\times 100$ lattice sites. The scaling behavior of the level statistics is examined for large spacings near the delocalization-localization transition and the correlation length exponent is found. By using high-precision calculations we conjecture a new interpolation of the critical cumulative probability, which has size-independent asymptotic form $\ln I\left(s\right)\propto {-s}^{\alpha }$ with $\alpha =1.0\mathrm{}\pm 0.1$.