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

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 [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 [Phys Rev. E 57, 5060 (1998)]. We also show that the isotropic two-component AB --> [symbol: see text] model is insensitive to reaction disorder, and that only logarithmic corrections arise, induced by strong disorder in the diffusion rate.