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

Saberi, A. A.; Niry, M. D.; Fazeli, S. M.; Tabar, M. R. Rahimi; Rouhani, S.

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

Authors

Description

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.
4 pages, 6 figures