One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder

TL;DR

This study uses large-scale simulations to investigate how quenched disorder affects the critical behavior of a one-dimensional, spin-anisotropic kinetic Ising model, revealing disorder's significant impact under specific conditions.

Contribution

It demonstrates the influence of quenched disorder on the phase transition and critical behavior of a one-dimensional kinetic Ising model with broken spin symmetry, highlighting regimes with Griffiths-like effects.

Findings

Disorder affects critical behavior mainly when diffusion is nearly blocked.

Critical behavior resembles that of the diluted contact process with Griffiths effects.

The isotropic AB -> 0 model is insensitive to reaction-disorder, with only logarithmic corrections.

Abstract

Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one dimensional, non-equilibrium kinetic Ising models with locally broken spin symmetry, at zero temperature (the symmetry is broken through spin-flip rates that differ for '+' and '-' spins). The model is found to exhibit a continuous phase transition to an absorbing state. The associated critical behavior is studied at zero branching rate of kinks, through analysis spreading of '+' and '-' spins and, of the kink density. Impurities exert a strong effect on the critical behavior only for a particular choice of parameters, corresponding to the strongly spin-anisotropic kinetic Ising model introduced by Majumdar et al. Typically, disorder effects become evident for impurity strengths such that diffusion is nearly blocked. In this regime, the critical behavior is similar to that arising, for example, in the one-dimensional diluted contact process, with Griffiths-like behavior for the kink density. We find variable cluster exponents, which obey a hyperscaling relation, and are similar to those reported by Cafiero et al. We also show that the isotropic two-component AB -> 0 model is insensitive to reaction-disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.