Abstract
Crossover scaling of the surface width in the Kardar-Parisi-Zhang equation for surface growth is studied numerically. By means of a perturbative solution of the discretized equation and by comparison with the exact solution of the corresponding linear equation, the finite-size effects due to the spatial discretization are carefully analyzed. The dependence on the nonlinearity of both the finite-size and asymptotic scaling forms is then investigated.
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Forrest, B.M., Toral, R. Crossover and finite-size effects in the (1+1)-dimensional Kardar-Parisi-Zhang equation. J Stat Phys 70, 703–720 (1993). https://doi.org/10.1007/BF01053591
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DOI: https://doi.org/10.1007/BF01053591