Anomalous Dimension and Spatial Correlations in a Point-Island Model
Abstract
We examine the island size distribution function and spatial correlation function of a model for island growth in the submonolayer regime in both one and two dimensions. The islands do not grow in shape and there is no flux of adatoms during the growth. We study the cases of various critical island sizes i for nucleation as a function of initial coverage. We found anomalous dimension of the island size distribution for large i. A many body random walk theory is presented to explain the anomaly. Using a version of mean-field theory we also obtain a closed form for the spatial correlation function. Our analytic results are verified by Monte Carlo simulations.
- Publication:
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Physical Review Letters
- Pub Date:
- March 1997
- DOI:
- 10.1103/PhysRevLett.78.1747
- arXiv:
- arXiv:cond-mat/9606092
- Bibcode:
- 1997PhRvL..78.1747L
- Keywords:
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- Condensed Matter