# Critical percolation in the ordering kinetics of twisted nematic phases

Source: [Critical percolation in the ordering kinetics of twisted nematic phases](<https://www.sota2.com/research/paper/68fa46161e209131ce91d9fd>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T05:37:50.378Z

Authors: Renan A. L. Almeida

Published: 2023-06-20T16:50:08.000Z

## 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 $t\_{\\textrm{p}}$. 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2306.11672>)

[PDF](<https://arxiv.org/pdf/2306.11672.pdf>)