Critical properties in long-range hopping Hamiltonians
| dc.creator | Cuevas, E. | |
| dc.date | 2004-07-07 | |
| dc.date.accessioned | 2026-07-07T02:59:04Z | |
| dc.date.available | 2026-07-07T02:59:04Z | |
| dc.description | Some properties of $d$-dimensional disordered models with long-range random hopping amplitudes are investigated numerically at criticality. We concentrate on the correlation dimension $d_2$ (for $d=2$) and the nearest level spacing distribution $P_c(s)$ (for $d=3$) in 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 (i) the extrapolated values of $d_2$ are of the form $d_2=c_db^d$ in the strong coupling limit and $d_2=d-a_d/b^d$ in the case of weak coupling, and (ii) $P_ (s)$ has the asymptotic form $P_c(s)\sim\exp (-A_ds^α)$ for $s\gg $, with the critical exponent $α=2-a_d/b^d$ for $b^d \gg 1$ and $α=1+c_d b^d$ for $b^d \ll 1$. In these cases the numerical coefficients $A_d$, $a_d$ and $c_d$ depend only on the dimensionality. | |
| dc.description | 9 pages, 6 .eps figures, contribution to the Festschrift for Michael Schreiber's 50th birthday | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0407168 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0407168 | |
| dc.identifier | phys. stat. sol. (b) 241, 2109 (2004) | |
| dc.identifier | doi:10.1002/pssb.200404783 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/24369 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.title | Critical properties in long-range hopping Hamiltonians | |
| dc.type | text |