title: Phase transition in the Ising model on a small-world network with distance-dependent interactions.
abstract: We study the collective behavior of an Ising system on a small-world network with the interaction J(r) proportional to r(-alpha), where r represents the Euclidean distance between two nodes. In the case of alpha=0 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 (alpha-->infinity) does not exhibit long-range order at any finite temperature. The Monte Carlo simulations are performed at various values of alpha, and the critical value alpha(c) beyond which the long-range order does not emerge is estimated to be 0. Thus, concluded is the absence of a phase transition in the system with the algebraically decaying interaction r(-alpha) for any nonzero positive value of alpha.
authors.affiliation: Department of Physics, Seoul National University, Seoul 151-747, Korea.
authors.forename: Daun
authors.initials: D
authors.lastname: Jeong
authors.forename: H
authors.initials: H
authors.lastname: Hong
authors.forename: Beom Jun
authors.initials: BJ
authors.lastname: Kim
authors.forename: M Y
authors.initials: MY
authors.lastname: Choi