Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-04-20
Phys. Rev. B 71, 024205 (2005)
Physics
Condensed Matter
Disordered Systems and Neural Networks
RevTex4, 7 two-column pages, 6 .eps figures, 1 table. A new section devoted to the spectral compressibility added. To be publi
Scientific paper
10.1103/PhysRevB.71.024205
The two-level correlation function $R_{d,\beta}(s)$ of $d$-dimensional disordered models ($d=1$, 2, and 3) with long-range random-hopping amplitudes is investigated numerically at criticality. We focus on models with orthogonal ($\beta=1$) or unitary ($\beta=2$) symmetry in 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 $R_{d,\beta}(s)$ is of the form $R_{d,\beta}(s)=1+\delta(s)-F_{\beta}(s^{\beta}/b^{d\beta})$, where $F_{1}(x)=\text{erfc}(a_{d,\beta} x)$ and $F_{2}(x)=\exp (-a_{d,\beta} x^2)$, with $a_{d,\beta}$ being a numerical coefficient depending on the dimensionality and the universality class. Finally, the level number variance and the spectral compressibility are also considerded.
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