Phase transition in the Ising model on a small-world network with distance-dependent interactions.
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.
Jeong
Daun
D
Department of Physics, Seoul National University, Seoul 151-747, Korea.
Hong
H
H
Kim
Beom Jun
BJ
Choi
M Y
MY