Weak pinning: surface growth in the presence of a defect

F. Slanina and M. Kotrla

Physica A: Statistical Mechanics and its Applications, 1998, vol. 256, issue 1, 1-17

Abstract: We study the influence of a point defect on the profile of a growing surface in the single-step growth model. We employ the mapping to the asymmetric exclusion model with blockage, and using Bethe-ansatz eigenfunctions as a starting approximation we are able to solve this problem analytically in two-particle sector. The dip caused by the defect is computed. A simple renormalization group-like argument enables to study scaling of the dip with increasing length of the sample L. For a horizontal surface we found that the surface is only weakly pinned at the inhomogeneity; the dip scales as a powerlaw Lγ with γ=0.58496. The value of the exponent agrees with direct numerical simulations of the inhomogeneous single-step growth model. In the case of tilted surfaces we observe a phase transition between weak and strong pinning and the exponent in the weak pinning regime depends on the tilt.

Keywords: Growth; Asymmetric exclusion model; Pinning (search for similar items in EconPapers)
Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:256:y:1998:i:1:p:1-17

DOI: 10.1016/S0378-4371(98)00203-9

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