Conformal Curves on $WO_3$ Surface

Details Conformal Curves on $WO_3$ Surface Conformal Curves on $WO_3$ Surface

2007-12-18

arxiv.org/abs/0712.2984v1

Phys. Rev. Lett. 100, 044504 (2008)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 6 figures. accepted in PRL

Scientific paper

10.1103/PhysRevLett.100.044504

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.

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