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

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

2008-03-07

arxiv.org/abs/0803.1051v1

Phys. Rev. E 77, 051607 (2008)

Physics

Data Analysis, Statistics and Probability

4 pages, 6 figures

Scientific paper

10.1103/PhysRevE.77.051607

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 $SLE_\kappa$) with diffusivity $\kappa=8/3$. It is shown that the absence of the non-linear term in the KPZ equation will change the diffusivity $\kappa$ 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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