Non-equilibrium Phase Transitions in 2D Small-World Networks: Competing Dynamics

Wei Liu,Gaoliang Zhou,Zhengxin Yan

doi:10.1515/phys-2019-0001

Abstract

Abstract This article offers a detailed analysis of the Ising model in 2D small-world networks with competing Glauber and Kawasaki dynamics. The non-equilibrium stationary state phase transitions are obtained in these networks. The phase transitions are discussed, and the phase diagrams are obtained via Monte Carlo simulations and finite-size analyzing. We find that as the addition of links increases the phase transition temperature increases and the transition competing probability of tricritical point decreases. For the competition of the two dynamics, ferromagnetic to anti-ferromagnetic phase transitions and the critical endpoints are found in the small-world networks.

Highlights

The dynamical behavior of the Ising model was successfully described with the Glauber [1] and Kawasaki [2] mechanisms
This article offers a detailed analysis of the Ising model in 2D small-world networks with competing Glauber and Kawasaki dynamics
Using extensive MC simulations, we have studied the nonequilibrium phase transitions in 2D small-world networks (SWN) governed by the competing Glauber and Kawasaki mechanism

Summary

Introduction

The dynamical behavior of the Ising model was successfully described with the Glauber [1] and Kawasaki [2] mechanisms. An interesting problem has been attracting much attention, i.e., the competing Glauber-type and Kawasaki-type dynamics, which leads to non-equilibrium steady states [3,4,5,6] This competing mechanism has been applied to the other spin models [7,8,9,10] as well, and the emergence of the dynamical tricritical point and self-organization have been reported. They can be realized by introducing a very small portion of long-range links to a regular lattice Such networks appear as small-worlds like random graphs, i.e., with a short average node-node distance that grows logarithmically with the network size.

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