Abstract
We investigate a discrete-time kinetic model without detailed balance which simulates the phase segregation of a quenched binary alloy. The model is a variation on the Rothman-Keller cellular automaton in which particles of type A (B) move toward domains of greater concentration of A (B). Modifications include a fully occupied lattice and the introduction of a temperature-like parameter which endows the system with a stochastic evolution. Using computer simulations, we examine domain growth kinetics in the two-dimensional model. For long times after a quench from disorder, we find that the average domain sizeR(t) ∼ t 1/3, in agreement with the prediction of Lifshitz-Slyozov-Wagner theory. Using a variety of methods, we analyze the critical properties of the associated second-order transition. Our analysis indicates that this model does not fall within either the Ising or mean-field classes.
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Alexander, F.J., Edrei, I., Garrido, P.L. et al. Phase transitions in a probabilistic cellular automaton: Growth kinetics and critical properties. J Stat Phys 68, 497–514 (1992). https://doi.org/10.1007/BF01341759
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DOI: https://doi.org/10.1007/BF01341759