  The two-dimensional (2d) Ising model is the statistical physics textbook
example for phase transitions and their kinetics. Quenched through the Curie
point with Glauber rates, the late-time description of the ferromagnetic domain
coarsening finds its place at the scalar sector of the Allen-Cahn (Model A)
class. Resisting exact results sought since Lifshitz's account in 1962, central
quantities in 2d Model A $-$ most scaling exponents and correlation functions
$-$ remain known up to approximate theories whose disparate outcomes urge
experimental assessment. Here, we perform such assessment from a comprehensive
study of the coarsening of 2d twisted nematic liquid crystals whose kinetics is
induced by a super-fast switching from a spatiotemporally chaotic state to a
two-phase concurrent, equilibrium one. Tracking the dynamics via optical
microscopy, we firstly show the sharp evidence of well-established Model A
aspects, such as the dynamic exponent $z=2$ and the dynamic scaling hypothesis,
to then move forward. We confirm the Bray-Humayun theory for Porod's regime
describing intradomain length scales of spatial correlators, and show that
their nontrivial decay beyond that regime is captured in a free-from-parameter
fashion by Gaussian theories. These paradigmatic theories, however, do not
perform well for time-related Model A statistics. We reveal that the collapsed
form of two-time correlators is best accounted for by the local scaling
invariance theory, along with the Fisher-Huse conjecture. We also suggest the
true value for the local persistence exponent, in disfavour of Gaussian models,
and extract a universal fractal dimension for the morphology of persistence
clusters that is notably close to the golden ratio. Given its accuracy and
possibilities, this experimental setup may work as a prototype to address
universality issues in the realm of nonequilibrium systems.
