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Conformal invariance of isoheight lines in a two-dimensional Kardar-Parisi-Zhang surface

Saberi, A. A ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1103/PhysRevE.77.051607
  3. Publisher: 2008
  4. Abstract:
  5. The statistics of isoheight lines in the (2+1) -dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformally invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of exact analytical results for the KPZ dynamics. We present direct evidence that the isoheight lines can be described by the family of conformally invariant curves called Schramm-Loewner evolution (or SLEI) with diffusivity Î=8/3. It is shown that the absence of the nonlinear term in the KPZ equation will change the diffusivity I from 8/3 to 4, indicating that the isoheight lines of the Edwards-Wilkinson surface are also conformally invariant and belong to the universality class of domain walls in the O (2) spin model. © 2008 The American Physical Society
  6. Keywords:
  7. Curve fitting ; Invariance ; Nonlinear analysis ; Random processes ; Edwards-Wilkinson surface ; Schramm-Loewner evolution (SLEI) ; Surface analysis
  8. Source: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics ; Volume 77, Issue 5 , 2008 ; 15393755 (ISSN)
  9. URL: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.77.051607