### Abstract

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 language | English (US) |
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Pages (from-to) | 377-403 |

Number of pages | 27 |

Journal | Journal of Statistical Physics |

Volume | 100 |

Issue number | 1-2 |

State | Published - Jul 1 2000 |

### Keywords

- 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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## Cite this

*Journal of Statistical Physics*,

*100*(1-2), 377-403.