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Classification of (2+1) -dimensional growing surfaces using Schramm-Loewner evolution.

A A Saberi1, H Dashti-Naserabadi, S Rouhani

  • 1Institute for Research in Fundamental Sciences, Tehran, Iran. a_saberi@ipm.ir

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary

Investigating isoheight lines in 2D growth models using Schramm-Loewner evolution (SLE), this study finds ballistic deposition, Eden, and RSOS models share universality with self-avoiding walks (SAW) and the Kardar-Parisi-Zhang (KPZ) equation.

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Area of Science:

  • Statistical physics
  • Surface growth phenomena
  • Conformal field theory

Background:

  • Two-dimensional surface growth models exhibit diverse universality classes.
  • The universality of ballistic deposition (BD), Eden, and restricted solid-on-solid (RSOS) models remains debated.
  • Schramm-Loewner evolution (SLE) provides a framework for analyzing critical phenomena.

Purpose of the Study:

  • To investigate the statistical behavior and scaling properties of isoheight lines in BD, Eden, and RSOS models.
  • To determine the universality class of these discrete growth models.
  • To connect these models to established theoretical frameworks like self-avoiding random walks (SAW) and the Kardar-Parisi-Zhang (KPZ) equation.

Main Methods:

  • Analysis of isoheight lines in saturated 2D surfaces.
  • Application of Schramm-Loewner evolution (SLE_{κ}) concepts.
  • Comparison of scaling properties with known universality classes.

Main Results:

  • Evidence suggests isoheight lines in BD, Eden, and RSOS models exhibit conformal invariance.
  • These models appear to belong to the same universality class as self-avoiding random walks (SAW), characterized by SLE_{8/3}.
  • The findings indicate a shared universality class with the two-dimensional Kardar-Parisi-Zhang (KPZ) equation.

Conclusions:

  • Discrete 2D growth models (BD, Eden, RSOS) fall into a single universality class.
  • This class is consistent with that of self-avoiding random walks (SAW) and the Kardar-Parisi-Zhang (KPZ) equation.
  • The study unifies the understanding of these fundamental surface growth models.