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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.

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.

Suggested Citation

  • Mendonça, J. Ricardo G., 2012. "Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6463-6469.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:24:p:6463-6469
    DOI: 10.1016/j.physa.2012.07.069
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    1. 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.
    2. 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;EDP Sciences, vol. 41(2), pages 223-230, September.
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