Critical level spacing distribution in long-range hopping Hamiltonians

Details Critical level spacing distribution in long-range hopping Hamiltonians Critical level spacing distribution in long-range hopping Hamiltonians

2003-10-31

arxiv.org/abs/cond-mat/0310774v2

Europhys. Lett. 67, 84 (2004)

Physics

Condensed Matter

Disordered Systems and Neural Networks

EPL style, 7 pages, 4 .eps figures, to be published in Europhys. Lett

Scientific paper

10.1209/epl/i2004-10048-2

The nearest level spacing distribution $P_c(s)$ 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 $P_c(s)$ has the asymptotic form $P_c(s)\sim\exp [-A_ds^{\alpha}]$ 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.

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