We present an analytic nonlinear-response approximation which yields
estimates for the field, temperature, and orientation dependences of the
velocity of an interface in a two-dimensional kinetic Ising model, driven
by a nonzero field at temperatures below the bulk critical temperature.
The interface mobility depends on the local interface structure,
and the Solid-on-Solid (SOS) approximation is used to estimate field-dependent
mean spin-class populations, from which the mean interface velocity can be
obtained for any specific single-spin-flip dynamic. In the low-temperature
limit the standard polynuclear-growth and single-step models are
recovered for interfaces making small and large angles with the
latice-symmetry directions, respectively. In the case of the Glauber
dynamic the analytic results are compared with Monte Carlo simulations.
Very satisfactory agreement is found in a wide range of field, temperature,
and interface orientation, both for the Ising model and for a modified model
in which the interface is constrained to maintain an SOS configuration at all
times. For the latter model we also present results for the correlations
between nearest-neighbor step heights, illustrating how the up-down symmetry
of the interface is gradually destroyed as the field is increased.
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