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arXiv · 1007.4000

Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution

A. A. Saberi·H. Dashti-Naserabadi·S. Rouhani
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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.

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A. A. Saberi, H. Dashti-Naserabadi, S. Rouhani. 2010-07-22. Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution. https://doi.org/10.1103/physreve.82.020101

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