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Physical Review E

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Surface growth on diluted lattices by a restricted solid-on-solid model

Changhan Lee and Sang Bub Lee^*

Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea

^*Corresponding author; sblee@knu.ac.kr

Phys. Rev. E 80, 021134 – Published 28 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.021134

Abstract

An influence of diluted sites on surface growth has been investigated, using the restricted solid-on-solid model. It was found that, with respect to equilibrium growth, the surface width and the saturated width exhibited universal power-law behaviors, i.e., $W \sim t^{β}$ and $W_{sat} \sim L^{ζ}$ , regarding all cases with respect to the concentration of diluted sites $x = 1 - p$ , with $p$ being the occupation probability on each lattice site. For $x < x_{c}$ ( $= 1 - p_{c}$ , $p_{c}$ being the percolation threshold), the growth appeared to be similar to that of a regular lattice, both in two and three dimensions. For $x = x_{c}$ , the growth yielded nontrivial exponents which were different from those on a regular lattice. In nonequilibrium growth, a considerable amount of diluted sites $(x \leq x_{c})$ appeared to yield nonuniversal growth, unlike the case of a regular lattice. The cause of nonuniversal growth dynamics has been investigated, considering the growth on a backbone cluster and on lattices constructed with periodically and randomly diluted subcells.

Article Text

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