1. Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution
- Author
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Saberi, A. A., Dashti-Naserabadi, H., and Rouhani, S.
- Subjects
Mathematics::Probability ,Statistical Mechanics (cond-mat.stat-mech) ,Condensed Matter::Statistical Mechanics ,FOS: Physical sciences ,Condensed Matter - Statistical Mechanics - Abstract
Statistical behavior and scaling properties of iso-height lines in three different saturated two-dimensional grown surfaces with controversial universality classes are investigated using ideas from Schramm-Loewner evolution (SLE$_\kappa$). We present some evidence that the iso-height lines in the ballistic deposition (BD), Eden and restricted solid-on-solid (RSOS) models have conformally invariant properties all in the same universality class as the self-avoiding random walk (SAW), equivalently SLE$_{8/3}$. This leads to the conclusion that all these discrete growth models fall into the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in two dimensions., Comment: 4 pages, 5 figures, to appear as a Rapid Communication in Phys. Rev. E
- Published
- 2010
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