Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2107.09043

Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals

Renan A. L. Almeida·Kazumasa A. Takeuchi
View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

cond-mat.stat-mechcond-mat.soft

Keep this discovery

BibTeXRIS

Renan A. L. Almeida, Kazumasa A. Takeuchi. 2021-07-19. Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals. https://doi.org/10.1103/physreve.104.054103

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗
arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗
arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗