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Analytic Approximations for the Velocity of Field-Driven Ising Interfaces

By Per Arne Rikvold and M. Kolesik


We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order-disorder phase transformations driven by a bulk free-energy difference. The Solid-on-Solid (SOS) approximation for the microscopic surface structure is used to estimate mean spin-class populations, from which the mean interface velocity can be obtained for any specific single-spin-flip dynamic. This linear-response approximation remains accurate for higher temperatures than the single-step and polynuclear growth models, while it reduces to these in the appropriate low-temperature limits. The equilibrium SOS approximation is generalized by mean-field arguments to obtain field-dependent class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.Comment: LaTex 24 pages with embedded postscript figures. J. Stat. Phys. in press. Minor revisions and two added references rel to V2, typo removed from V

Topics: Condensed Matter - Statistical Mechanics, Condensed Matter - Materials Science
Year: 2000
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