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

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 SLE_{kappa} ) with diffusivity kappa=8/3 . It is shown that the absence of the nonlinear term in the KPZ equation will change the diffusivity kappa 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.

• Publication year

  2008

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2008-03-07

• Fields of study

  Mathematics, Physics, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.77.051607arXiv 0803.1051PMID 18643079
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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