One Dimensional Nonequilibrium Kinetic Ising Models with Branching Annihilating Random Walk

TL;DR

This paper investigates a one-dimensional nonequilibrium kinetic Ising model with branching and annihilating random walks, revealing a phase transition characterized by critical exponents consistent with cellular automata results.

Contribution

It introduces a novel kinetic Ising model with branching and annihilation dynamics, connecting it to known cellular automata universality classes.

Findings

Steady states are governed by branching annihilating random walks.

Critical exponents match those of Grassberger's cellular automata.

Phase transition behavior is characterized through numerical simulations.

Abstract

Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges at $T=\infty$ are investigated numerically from the point of view of a phase transition. Branching annihilating random walk of the ferromagnetic domain boundaries determines the steady state of the system for a range of parameters of the model. Critical exponents obtained by simulation are found to agree, within error, with those in Grassberger's cellular automata.