On the properties of small-world network models |
| |
Authors: | A. Barrat M. Weigt |
| |
Affiliation: | (1) Laboratoire de Physique Théorique, batiment 210, Université Paris-Sud, 91405 Orsay Cedex, France, FR;(2) CNRS-Laboratoire de Physique Théorique de l'E.N.S., 24 rue Lhomond, 75231 Paris Cedex 05, France, FR |
| |
Abstract: | We study the small-world networks recently introduced by Watts and Strogatz [Nature 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. [0.5cm] Received 29 March 1999 and Received in final form 21 May 1999 |
| |
Keywords: | PACS. 05.50.+q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations statistical mechanics of model systems - 05.70.Fh Phase transitions: general studies |
本文献已被 SpringerLink 等数据库收录! |
|