Critical percolation in the ordering kinetics of twisted nematic phases

Abstract

I report on the experimental confirmation that critical percolation statistics underlie the ordering kinetics of twisted nematic phases in the Allen-Cahn universality class. Soon after the ordering starts from a homogeneous disordered phase and proceeds towards a broken ${\mathbb{Z}}_2$-symmetry phase, the system seems to be attracted to the random percolation fixed point at a special timescale $t_{\text{p}}$. At this time, exact formulae for crossing probabilities in percolation theory agree with the corresponding probabilities in the experimental data. The ensuing evolution for the number density of hull-enclosed areas is described by an exact expression derived from a percolation model endowed with curvature-driven interface motion. Scaling relation for hull-enclosed areas versus perimeters reveals that the fractal percolation geometry is progressively morphed into a regular geometry up to the order of the classical coarsening length. In view of its universality and experimental possibilities, the study opens a path for exploring percolation keystones in the realm of nonequilibrium, phase-ordering systems.

References in corpus (8)

• Exact results for curvature-driven coarsening in two dimensions
• Domain growth morphology in curvature driven two dimensional coarsening
• Experimental test of curvature-driven dynamics in the phase ordering of a two dimensional liquid crystal
• Maximal Diversity and Zipf's Law
• Asymptotic States of Ising Ferromagnets with Long-range Interactions
• On Crossing Event Formulas in Critical Two-Dimensional Percolation
• Dynamical cluster size heterogeneity
• Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model

Cited by in corpus (4)

• Opinion inertia and coarsening in the Persistent Voter model
• Critical clusters in liquid crystals: Fractal geometry and conformal invariance
• Coarsening in the Persistent Voter Model: analytical results
• Cluster percolation in the three-dimensional $\pm J$ random-bond Ising model