One-dimensional Ising model built on small-world networks: competing dynamics

TL;DR

This paper analyzes the dynamics of a one-dimensional Ising model on small-world networks, exploring how competing Glauber and Kawasaki mechanisms affect phase behavior and dynamical properties influenced by the small-world effect.

Contribution

It introduces a combined dynamic analysis of Glauber and Kawasaki mechanisms on small-world networks, revealing their impact on phase diagrams and system behavior.

Findings

Small-world effect influences phase transitions.

Competing dynamics alter the phase diagram.

Rewiring-type networks show similar results to adding-type networks.

Abstract

In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result of rewiring-type is given because of the similarities of these two typical networks. We study the dynamical processes with competing Glauber mechanism and Kawasaki mechanism. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. By studying the phase diagram obtained in the present work, we can realize some dynamical properties influenced by the small-world effect.