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.
Saberi
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AA
Department of Physics, Sharif University of Technology, Tehran 11155-9161, Iran.
Niry
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MD
Fazeli
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SM
Rahimi Tabar
M R
MR
Rouhani
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S