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

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 $SL{E}_{\kappa }$) 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.

4 pages, 6 figures

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• 2D growth processes: SLE and Loewner chains
• Stochastic geometry of critical curves, Schramm-Loewner evolutions, and conformal field theory
• Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?
• Conformal Curves on $W{O}_3$ Surface
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Cited by in corpus (6)

• Recent advances in percolation theory and its applications
• Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution
• Thermal Behavior of Spin Clusters and Interfaces in two-dimensional Ising Model on Square Lattice
• Three Dimensional Ising Model, Percolation Theory and Conformal Invariance
• Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface
• Loewner driving functions for off-critical percolation clusters