Analytic approximations for the velocity of field-driven Ising interfaces

Per Arne Rikvold, M. Kolesik

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


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 spin-class populations for moving interfaces, and thereby a nonlinear-response approximation for the velocity. The analytic results for the interface velocity and the spin-class populations are compared with Monte Carlo simulations. Excellent agreement is found in a wide range of field, temperature, and interface orientation.

Original languageEnglish (US)
Pages (from-to)377-403
Number of pages27
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Jul 2000


  • Interface dynamics
  • Kinetic Ising model
  • Linear response
  • Microscopic interface structure
  • Monte Carlo simulation
  • Nonlinear response
  • Solid-on-solid (SOS) approximation
  • Surface anisotropy
  • Surface growth

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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