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 $J(r)\propto r^{-\alpha }$, 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 $(\alpha \to \infty )$ does not exhibit long-range order at any finite temperature. 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 zero. 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 $\alpha$.

References in corpus (5)

• Statistical mechanics of complex networks
• Evolution of networks
• XY model in small-world networks
• The boundary between long-range and short-range critical behavior
• Comment on "Ising model on a small world network"

Cited by in corpus (14)

• Critical phenomena in complex networks
• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Performance of networks of artificial neurons: The role of clustering
• Quantifying the connectivity of a network: The network correlation function method
• Scaling in Small-World Resistor Networks
• Synchronization Landscapes in Small-World-Connected Computer Networks
• Phase transitions in Ising model on a Euclidean network
• Magnetic models on various topologies
• Phase transition of a one-dimensional Ising model with distance-dependent connections
• Magnetic Small World Nanomaterials: Physical Small World Networks
• Phase transitions in Ising model induced by weight redistribution on weighted regular networks
• Potts model with q=3 and 4 states on directed Small-World network
• Synchronization in Small-World-Connected Computer Networks
• Quantum magnetism on small-world networks