Critical clusters in liquid crystals: Fractal geometry and conformal invariance

Abstract

We study the two-dimensional domain morphology of twisted nematic liquid crystals during their phase-ordering kinetics [R. A. L. Almeida, Phys. Rev. Lett. 131 (2023) 268101], which is a physical candidate to self-generate critical clusters in the percolation universality class. Here we present experimental evidence that large clusters and their hulls are indeed both fractals with dimensions of the corresponding figures in critical percolation models. The asymptotic decay of a crossing probability, from a region in the vicinity of the origin to the boundary of disks, is described by the Lawler-Schramm-Werner theorem provided that a microscopic length in the original formulation is replaced by the coarsening length of the liquid crystal. Furthermore, the behavior for the winding angle of large loops is, at certain scales, compatible with that of Schramm-Loewner evolution curves with diffusivity $\kappa = 6$. These results show an experimental realization of critical clusters in phase ordering.