Phase transition in the Ising model on a small-world network with distance-dependent interactions
Statistical Mechanics
2009-11-10 v1
Abstract
We study the collective behavior of an Ising system on a small-world network with the interaction , where represents the Euclidean distance between two nodes. In the case of corresponding to the uniform interaction, the system is known to possess a phase transition of the mean-field nature, while the system with the short-range interaction does not exhibit long-range order at any finite temperature. Monte Carlo simulations are performed at various values of , and the critical value beyond which the long-range order does not emerge is estimated to be zero. Thus concluded is the absence of a phase transition in the system with the algebraically decaying interaction for any nonzero positive value of .
Keywords
Cite
@article{arxiv.cond-mat/0306017,
title = {Phase transition in the Ising model on a small-world network with distance-dependent interactions},
author = {Daun Jeong and H. Hong and Beom Jun Kim and M. Y. Choi},
journal= {arXiv preprint arXiv:cond-mat/0306017},
year = {2009}
}