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arXiv · 0803.1051

Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface

A. A. Saberi·M. D. Niry·S. M. Fazeli·M. R. Rahimi Tabar·S. Rouhani
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Abstract

The statistics of the iso-height lines in (2+1)-dimensional Kardar-Parisi-Zhang (KPZ) model is shown to be conformal invariant and equivalent to those of self-avoiding random walks. This leads to a rich variety of new exact analytical results for the KPZ dynamics. We present direct evidence that the iso-height lines can be described by the family of conformal invariant curves called Schramm-Loewner evolution (or $SLE_κ$) with diffusivity $κ=8/3$. It is shown that the absence of the non-linear term in the KPZ equation will change the diffusivity $κ$ from 8/3 to 4, indicating that the iso-height lines of the Edwards-Wilkinson (EW) surface are also conformally invariant, and belong to the universality class of the domain walls in the O(2) spin model.

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A. A. Saberi, M. D. Niry, S. M. Fazeli, M. R. Rahimi Tabar, S. Rouhani. 2008-03-07. Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface. https://doi.org/10.1103/physreve.77.051607

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