Conformal Curves on $WO_3$ Surface

TL;DR

This study demonstrates that iso-height lines on the WO_3 surface are conformally invariant curves consistent with SLE_{kappa} with kappa around 3, marking the first experimental observation of such curves.

Contribution

The paper provides the first experimental evidence of conformally invariant curves on a physical surface, linking them to SLE and proposing Ballistic Deposition as a growth model.

Findings

Iso-height lines on WO_3 are conformally invariant.

These lines follow SLE_{kappa} with kappa ~ 3.

Ballistic Deposition can produce similar contour statistics.

Abstract

We have studied the iso-height lines on the $\mathrm{WO_3}$ 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 $SLE_{\kappa}$), 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.