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Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

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  • Mendonça, J. Ricardo G.
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    Abstract

    We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar–Parisi–Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0378437112007601
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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 391 (2012)
    Issue (Month): 24 ()
    Pages: 6463-6469

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    Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6463-6469

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Stochastic Ising model; Bethe ansatz; RSOS growth model; Zero range process; Exclusion process; XXZ quantum chain; KPZ universality class;

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    1. M. Evans & E. Levine & P. Mohanty & D. Mukamel, 2004. "Modelling one-dimensional driven diffusive systems by the Zero-Range Process," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 41(2), pages 223-230, 09.
    2. Marchand, J.P. & Martin, Ph.A., 1984. "A microscopic derivation of the classical nucleation equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 127(3), pages 681-691.
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