Ising Model Scaling Behaviour on z-Preserving Small-World Networks
| dc.creator | Hawick, K. A. | |
| dc.creator | James, H. A. | |
| dc.date | 2006-11-29 | |
| dc.date.accessioned | 2026-07-07T07:31:31Z | |
| dc.date.available | 2026-07-07T07:31:31Z | |
| dc.description | We have investigated the anomalous scaling behaviour of the Ising model on small-world networks based on 2- and 3-dimensional lattices using Monte Carlo simulations. Our main result is that even at low $p$, the shift in the critical temperature $ΔT_c$ scales as $p^{s}$, with $s \approx 0.50$ for 2-D systems, $s \approx 0.698$ for 3-D and $s \approx 0.75$ for 4-D. We have also verified that a $z$-preserving rewiring algorithm still exhibits small-world effects and yet is more directly comparable with the conventional Ising model; the small-world effect is due to enhanced long-range correlations and not the change in effective dimension. We find the critical exponents $β$ and $ν$ exhibit a monotonic change between an Ising-like transition and mean-field behaviour in 2- and 3-dimensional systems. | |
| dc.description | 19 Pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0611763 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0611763 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118784 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Ising Model Scaling Behaviour on z-Preserving Small-World Networks | |
| dc.type | text |