Non-equilibrium phase transitions in one-dimensional kinetic Ising models

TL;DR

This paper investigates non-equilibrium phase transitions in one-dimensional kinetic Ising models, revealing how increasing interaction range or strength shifts the transition to mean-field type and identifying a tricritical point.

Contribution

It extends previous models by analyzing the effects of longer-range and stronger interactions on phase transition nature and locates a tricritical point at the Glauber limit.

Findings

Transition becomes mean-field type with increased exchange range/strength

A tricritical point is identified at the Glauber limit

Critical exponent β is approximately 1.0

Abstract

A family of nonequilibrium kinetic Ising models, introduced earlier, evolving under the competing effect of spin flips at {\it zero temperature} and nearest neighbour random spin exchanges is further investigated here. By increasing the range of spin exchanges and/or their strength the nature of the phase transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first order tricitical point is located at the Glauber ($\delta=0$) limit. Corrections to mean-field theory are evaluated up to sixth order in a cluster approximation and found to give good results concerning the phase boundary and the critical exponent $\beta$ of the order parameter which is obtained as $\beta\simeq1.0$.