Critical level spacing distribution in long-range hopping Hamiltonians

The nearest level spacing distribution $P_\ab{c}(s)$ of d-dimensional disordered models ($d=1$ and 2) with long-range random hopping amplitudes is investigated numerically at criticality. We focus on both the weak ($b^d\gg 1$) and the strong ($b^d\ll 1$) coupling regime, where the parameter $b^{-d}$ plays the role of the coupling constant of the model. It is found that $P_\ab{c}(s)$ has the asymptotic form $P_\ab{c}(s)\sim\exp[-A_ds^{\alpha}]$ for $s\gg 1$, with the critical exponent $\alpha=2-a_d/b^d$ in the weak-coupling limit and $\alpha=1+c_d b^d$ in the case of strong coupling