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Domain scaling and glassy dynamics in a one-dimensional Kawasaki Ising model

1991; American Physical Society; Volume: 44; Issue: 22 Linguagem: Inglês

10.1103/physrevb.44.12263

1095-3795

Stephen J. Cornell, Kimmo Kaski, R B Stinchcombe,

Stochastic processes and statistical mechanics

The one-dimensional spin-exchange kinetic Ising model is studied using approximations based on the motion of single spins. This model exhibits domain-scaling behavior after a deep quench to low temperatures, with the same scaling exponent (1/3) as in higher dimensions. Under slow cooling, the kink density of this system is predicted to freeze at a value proportional to ${\mathrm{\ensuremath{\tau}}}^{\mathrm{\ensuremath{-}}1/\mathit{z}}$, where \ensuremath{\tau} is the inverse cooling rate and z is the dynamic critical exponent (=5) for ``natural'' cooling programs. The results of Monte Carlo simulations are found to compare favorably with these predictions. The residual temporal behavior in a frozen nonequilibrium state is studied in the short- and long-time regimes, approaching asymptotically a stretched-exponential form.