Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-10-26
Physics
Condensed Matter
Statistical Mechanics
10 pages, 4 figures, references updated and minor changes in the text, to appear in Euro. Phys. J. B
Scientific paper
10.1140/epjb/e2002-00341-4
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the "perturbative" limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behavior. Possibilities of controlling this instability by introducing statistically "irrelevant" (in the sense of renormalization groups) higher ordered nonlinearities have also been discussed.
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