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

Nóra Menyhárd1 and Géza Ódor2

  • 1Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O. Box 49, Hungary
  • 2Research Institute for Technical Physics and Materials Science, H-1525 Budapest, P.O. Box 49, Hungary

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Phys. Rev. E 76, 021103 – Published 2 August, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.021103

Abstract

Large-scale Monte Carlo simulations are used to explore the effect of quenched disorder on one-dimensional, nonequilibrium 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. [Phys Rev. Lett 86, 2301 (2001)]. 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. [Phys Rev. E 57, 5060 (1998)]. We also show that the isotropic two-component AB→0̸ model is insensitive to reaction disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.

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Phys. Rev. E 76, 021103– Published 2 August, 2007
  • Received 21 December 2006

© 2007 American Physical Society

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