Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1511.02076

Scaling of local roughness distributions

Fabio D. A. Aarao Reis
View original source ↗Read source document ↗Export metadata ↓

Abstract

Local roughness distributions (LRDs) are studied in the growth regimes of lattice models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 and 2+1 dimensions and in a model of the Villain-Lai-Das Sarma (VLDS) growth class in 2+1 dimensions. The squared local roughness w_2 is defined as the variance of the height inside a box of lateral size r and the LRD P_r(w_2) is sampled as this box glides along a surface with size L >> r. The variation coefficient C and the skewness S of the distributions are functions of the scaled box size r / xi, where xi(t) is a correlation length. For r <~ 0.3 xi, plateaus of C and S are observed, but with a small time dependence. For a quantitative characterization of the universal LRD, extrapolation of these values with power-law corrections in time are performed. The reliability of this procedure is confirmed in 1+1 dimensions by comparison of results of the restricted solid-on-solid model and theoretically predicted values of Edwards-Wilkinson interfaces. For r >> xi, C and S vanish because the LRD converges to a Dirac delta function. This confirms the inadequacy of extrapolations of amplitude ratios to r -> infinity, as proposed in recent works. On the other hand, it highlights the advantage of scaling LRDs by the average instead of scaling by the variance due to the usually higher accuracy of C compared to S. The scaled LRD of the VLDS model is very close to the KPZ one due to the small difference between their variation coefficients and the plateaus of C and S are very narrow due to the slow time increase of xi. These results suggest that experimental LRDs obtained in short growth times and with limited resolution may be inconclusive to determine their universality classes if data accuracy is low and/or data extrapolation to the long time limit is not feasible.

Explore related subjects

cond-mat.stat-mechcond-mat.mes-hallcond-mat.mtrl-sci

Keep this discovery

BibTeXRIS

Fabio D. A. Aarao Reis. 2015-11-06. Scaling of local roughness distributions. https://doi.org/10.1088/1742-5468%2F2015%2F11%2Fp11020

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↗