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We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf-Cole solutions to the KPZ equation.

Mathematical Physics · Physics 2015-12-25 Martin Hairer , Jeremy Quastel

We investigate analytically the large dimensional behavior of the Kardar-Parisi-Zhang (KPZ) dynamics of surface growth using a recently proposed non-perturbative renormalization for self-affine surface dynamics. Within this framework, we…

Statistical Mechanics · Physics 2009-10-31 C. Castellano , A. Gabrielli , M. Marsili , M. A. Munoz , L. Pietronero

We present numerical Monte Carlo results for the stationary state properties of KPZ type growth in two dimensional surfaces, by evaluating the finite size scaling (FSS) behaviour of the 2nd and 4th moments, $W_2$ and $W_4$, and the…

Statistical Mechanics · Physics 2009-10-31 Chen-Shan Chin , Marcel den Nijs

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…

Statistical Mechanics · Physics 2015-12-09 Fabio D. A. Aarao Reis

We consider an infinite interface in $d>2$ dimensions, governed by the Kardar-Parisi-Zhang (KPZ) equation with a weak Gaussian noise which is delta-correlated in time and has short-range spatial correlations. We study the probability…

Statistical Mechanics · Physics 2018-05-02 Baruch Meerson , Pavel V. Sasorov , Arkady Vilenkin

The article [Phys. Rev. E {\bf 73}, 031111 (2006)] by Horowitz and Albano reports on simulations of competitive surface-growth models RD+X that combine random deposition (RD) with another deposition X that occurs with probability $p$. The…

Statistical Mechanics · Physics 2015-01-23 A. Kolakowska , M. A. Novotny

Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine…

Soft Condensed Matter · Physics 2016-08-31 S. V. Ghaisas

Long-range spatiotemporal correlations may play important roles in nonequilibrium surface growth process. In order to investigate the effects of long-range temporal correlation on dynamic scaling of growing surfaces, we perform extensive…

Statistical Mechanics · Physics 2021-08-11 Tianshu Song , Hui Xia

We consider the fluctuations in the stochastic growth of a one-dimensional interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the…

Disordered Systems and Neural Networks · Physics 2018-09-24 Jacopo de Nardis , Pierre Le Doussal

The competition between local Brownian roughness and global parabolic curvature experienced in many random interface models reflects an important aspect of the KPZ universality class. It may be summarised by an exponent triple…

Probability · Mathematics 2018-11-14 Riddhipratim Basu , Shirshendu Ganguly , Alan Hammond

We show numerically that the roughness and growth exponents of a wide range of rough surfaces, such as random deposition with relaxation (RDR), ballistic deposition (BD) and restricted solid-on-solid model (RSOS), are independent of the…

Statistical Mechanics · Physics 2013-04-09 S. Hosseinabadi , M. A. Rajabpour , M. Sadegh Movahed , S. M. Vaez Allaei

We study the aging property for stationary models in the KPZ universality class. In particular, we show aging for the stationary KPZ fixed point, the Cole-Hopf solution to the stationary KPZ equation, the height function of the stationary…

Probability · Mathematics 2020-09-04 Jean-Dominique Deuschel , Gregorio R. Moreno Flores , Tal Orenshtein

The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev-Petviashvili (KP) equation. This is derived algebraically from a Fredholm…

Probability · Mathematics 2023-04-26 Jeremy Quastel , Daniel Remenik

We investigate numerically the effects of long-range temporal and spatial correlations based on the rescaled distributions of the squared interface width $W^2(L,t)$ and the interface height $h(x,t)$ in the (1+1)-dimensional…

Statistical Mechanics · Physics 2025-02-25 Zhichao Chang , Hui Xia

The universal, scaled order parameter profiles $P_{\pm}(z/\xi)$ for critical adsorption of a fluid or fluid mixture onto a wall or interface, and for the extraordinary transition of the semi-infinite Ising model, are discussed…

Condensed Matter · Physics 2007-05-23 M. Smock , H. W. Diehl , D. P. Landau

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been…

Statistical Mechanics · Physics 2026-04-08 Ricardo Gutierrez , Rodolfo Cuerno

We describe a directed avalanche model; a slowly unloading sandbox driven by lowering a retaining wall. The directness of the dynamics allows us to interpret the stable sand surfaces as world sheets of fluctuating interfaces in one lower…

Statistical Mechanics · Physics 2009-11-07 Chun-Chung Chen , Marcel den Nijs

Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits.…

Statistical Mechanics · Physics 2014-01-27 Horacio S. Wio , Roberto R. Deza , Carlos Escudero , Jorge A. Revelli

We extend our 2+1 dimensional discrete growth model (PRE 79, 021125 (2009)) with conserved, local exchange dynamics of octahedra, describing surface diffusion. A roughening process was realized by uphill diffusion and curvature dependence.…

Statistical Mechanics · Physics 2010-05-14 Geza Odor , Bartosz Liedke , Karl-Heinz Heinig

The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our…

Statistical Mechanics · Physics 2018-05-29 Kazumasa A. Takeuchi