Conformal Curves on $W{O}_3$ Surface

Abstract

We have studied the iso-height lines on the $\mathrm{W}{\mathrm{O}}_3$ surface as a physical candidate for conformally invariant curves. We have shown that these lines are conformally invariant with the same statistics of domain walls in the critical Ising model. They belong to the family of conformal invariant curves called Schramm-Loewner evolution (or $SL{E}_{\kappa }$), with diffusivity of $\kappa \sim 3$. This can be regarded as the first experimental observation of SLE curves. We have also argued that Ballistic Deposition (BD) can serve as a growth model giving rise to contours with similar statistics at large scales.

4 pages, 6 figures. accepted in PRL

References in corpus (3)

• 2D growth processes: SLE and Loewner chains
• Are Domain Walls in Spin Glasses Described by Stochastic Loewner Evolutions?
• Nodal Domain Statistics for Quantum Maps, Percolation and SLE

Cited by in corpus (4)

• Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface
• Thermal Behavior of Spin Clusters and Interfaces in two-dimensional Ising Model on Square Lattice
• Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface
• Loewner driving functions for off-critical percolation clusters