On the properties of small-world network models
| dc.creator | Barrat, A. | |
| dc.creator | Weigt, M. | |
| dc.date | 1999-03-29 | |
| dc.date | 1999-08-25 | |
| dc.date.accessioned | 2026-07-07T03:13:08Z | |
| dc.date.available | 2026-07-07T03:13:08Z | |
| dc.description | We study the small-world networks recently introduced by Watts and Strogatz [Nature {\bf 393}, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a ``small-world'' behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a ``small-world'' one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite. | |
| dc.description | 19 pages including 15 figures, version accepted for publication in EPJ B | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9903411 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9903411 | |
| dc.identifier | Europ. Phys. J. B 13, 547 (2000) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/29181 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | On the properties of small-world network models | |
| dc.type | text |