The growth of order via domain coarsening is a long-standing instance of scale-invariant and universal phenomenon out-of-equilibrium [1]. Over a half-century of continuous interest, the theory for phase-ordering kinetics was formulated on the dynamic scaling hypothesis. Breakthroughs [2,3] evidenced the settling of critical percolation (CP) statistics along with the phase-ordering of two-dimensional systems with scalar, nonconserved (model A) kinetics. The CP-model-A theory culminated in an exact formula for the number density of hull areas [2], partially observed in [4], while the emergence of a percolative structure suggested modifications [3] in the celebrated scaling hypothesis. However, these prominent proposals, as well as their implications, require experimental validation. Here, we experimentally study such issues exploring domain coarsening of two-dimensional twisted nematic liquid crystals (TNLC). The ordering is triggered by a sudden transition between an electrically-driven turbulent state - comprising plenty of entangled topological defects - and a state free from applied fields and defects. The TNLC domain ordering proceeds by a curvature-driven shrinking of defects which, actually, separate domains of opposite chirality. Spatio-temporal configurations of the TNLC local order parameter follow the universal model A statistics. A morphological analysis of domain structures reveals that the number density of TNLC hulls per system area agrees with the exact CP-model-A formula within its full range, without any fit procedure. Additionally, we observe CP statistics in the scaling of the largest TNLC domain, which further reveals the existence of an additional, percolative-related length scale as observed in discrete model systems [3]. Our results validate the CP-model-A theory. They suggest a modification for the dynamic scaling hypothesis via the introduction of a new, percolation-related dynamic exponent that is here experimentally measured. Our results not only corroborates recent proposals based on discrete models [3] but also extend their validity for continuum model A systems.

[1] A. J. Bray, Adv. Phys. 51, 481 (2002).

[2] J. J. Arenzon, A. J. Bray, L. F. Cugliandolo, A. Sicilia, Phys. Rev. Lett. 98, 145701 (2007).

[3] T. Blanchard, F. Corberi, L. F. Cugliandolo, M. Picco, Europhys. Lett. 106, 66001 (2014).

[4] A. Sicilia et al., Phys. Rev. Lett. 101, 197801 (2008).