Phase transition of a one-dimensional Ising model with distance-dependent connections

Abstract

The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $\Theta (l)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through studying the Ising model on networks with different $m$ values, this paper discusses the impact of the global correlation, which decays with the increase of $m$, on the phase transition of the Ising model. Adding the analysis of the finite-size scaling of the order parameter $[<M>]$, it is observed that in the whole range of $0<m<2$, a finite-temperature transition exists, and the critical exponents show consistence with mean-field values, which indicates a mean-field nature of the phase transition.

5 pages,8 figures

References in corpus (15)

• Renormalization group analysis of the small-world network model
• Scaling and percolation in the small-world network model
• Ising model in small-world networks
• XY model in small-world networks
• Small-World Networks: Links with long-tailed distributions
• Comment on "Ising model on a small world network"
• Phase transitions in a network with range dependent connection probability
• Shortest paths on systems with power-law distributed long-range connections
• Exact Solution of Ising Model on a Small-World Network
• Small-world phenomena and the statistics of linear polymer networks
• Navigation in a small world with local information
• Phase transition in the Ising model on a small-world network with distance-dependent interactions
• Phase transitions in Ising model on a Euclidean network
• Introducing Small-World Network Effect to Critical Dynamics
• Complex structures in generalized small worlds

Cited by in corpus (5)

• Spatial Networks
• Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance
• Effect of the nature of randomness on quenching dynamics of Ising model on complex networks
• Susceptible-Infected-Recovered model on Euclidean network
• Complex Networks: effect of subtle changes in nature of randomness