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We study a model of corrosion and passivation of a metalic surface in contact with a solution using scaling arguments and simulation. The passive layer is porous so that the metal surface is in contact with the solution. The volume excess…

Materials Science · Physics 2009-11-11 Fabio D. A. Aarao Reis , Janusz Stafiej

We study the crossover between classical and nonclassical critical behaviors. The critical crossover limit is driven by the Ginzburg number G. The corresponding scaling functions are universal with respect to any possible microscopic…

Statistical Mechanics · Physics 2009-10-31 A. Pelissetto , P. Rossi , E. Vicari

We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with…

Statistical Mechanics · Physics 2007-05-23 Michael Praehofer , Herbert Spohn

We prove a Hausdorff dimension result for the image of two-dimensional multiplicative cascade processes, and we obtain from this result a KPZ-type formula which normally has one point of phase transition.

Probability · Mathematics 2012-09-26 Xiong Jin

We introduce a set of statistical measures that can be used to quantify non-equilibrium surface growth. They are used to deduce new information about spatiotemporal dynamics of model systems for spinodal decomposition and surface…

Statistical Mechanics · Physics 2009-11-10 Girish Nathan , Gemunu Gunaratne

We study a generalization of the Wolf-Villain (WV) interface growth model based on a probabilistic growth rule. In the WV model, particles are randomly deposited onto a substrate and subsequently move to a position nearby where the binding…

Statistical Mechanics · Physics 2015-03-19 S G Alves , J G Moreira

We analyze simulations results of a model proposed for etching of a crystalline solid and results of other discrete models in the 2+1-dimensional Kardar-Parisi-Zhang (KPZ) class. In the steady states, the moments W_n of orders n=2,3,4 of…

Statistical Mechanics · Physics 2009-11-10 Fabio D. A. Aarao Reis

We develop a scaling theory for KPZ growth in one dimension by a detailed study of the polynuclear growth (PNG) model. In particular, we identify three universal distributions for shape fluctuations and their dependence on the macroscopic…

Statistical Mechanics · Physics 2009-10-31 Michael Praehofer , Herbert Spohn

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are…

Statistical Mechanics · Physics 2012-10-29 Patrik L. Ferrari , Alexei Borodin

We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…

Statistical Mechanics · Physics 2019-02-15 Abbas Ali Saberi , Hor Dashti-N. , Joachim Krug

We determine the scaling functions describing the crossover from Ising-like critical behavior to classical critical behavior in two-dimensional systems with a variable interaction range. Since this crossover spans several decades in the…

Statistical Mechanics · Physics 2009-10-30 Erik Luijten , Henk W. J. Blöte , Kurt Binder

One of the main difficulties in proving convergence of discrete models of surface growth to the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than one is that the correct way to take a scaling limit, so that the limit is…

Probability · Mathematics 2022-11-30 Sourav Chatterjee

The domino-shuffling algorithm can be seen as a stochastic process describing the irreversible growth of a $(2+1)$-dimensional discrete interface. Its stationary speed of growth $v_{\mathtt w}(\rho)$ depends on the average interface slope…

Probability · Mathematics 2021-08-27 Sunil Chhita , Fabio Lucio Toninelli

The short time behavior of the 1+1 dimensional KPZ growth equation with a flat initial condition is obtained from the exact expressions of the moments of the partition function of a directed polymer with one endpoint free and the other…

Statistical Mechanics · Physics 2012-11-13 Thomas Gueudre , Pierre Le Doussal , Alberto Rosso , Adrien Henry , Pasquale Calabrese

The equilibrium crystal shape of a body-centered solid-on-solid (BCSOS) model on a honeycomb lattice is studied numerically. We focus on the facet ridge endpoints (FRE). These points are equivalent to one dimensional KPZ-type growth in the…

Statistical Mechanics · Physics 2009-10-31 Douglas Davidson , Marcel den Nijs

A nearest neighbour spin pair of the quasi-two-dimensional three-state Potts model interacts with the strength $J(>0)$ in the $xy$-plane and with $\lambda J$ $(0\le \lambda \ll 1)$ in the $z$-axis. The phase transition is of second-order…

Condensed Matter · Physics 2015-06-25 Atsushi Yamagata

We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the…

Statistical Mechanics · Physics 2009-11-07 Rodolfo Cuerno , Mario Castro

The crossover behavior of various models exhibiting phase transition to absorbing phase with parity conserving class has been investigated by numerical simulations and cluster mean-field method. In case of models exhibiting Z_2 symmetric…

Statistical Mechanics · Physics 2009-11-13 Geza Odor , Nora Menyhard

The asymmetric simple exclusion process and its analysis by mode coupling theory (MCT) is reviewed. To treat the weakly asymmetric case at large space scale $x\varepsilon^{-1}$, %(corresponding to small Fourier momentum at scale…

Statistical Mechanics · Physics 2023-06-27 G. M. Schütz

We consider dimensional crossover for an $O(N)$ Landau-Ginzburg-Wilson model on a $d$-dimensional film geometry of thickness $L$ in the large $N$-limit. We calculate the full universal crossover scaling forms for the free energy and the…

Condensed Matter · Physics 2009-10-28 Denjoe O'Connor , C. R. Stephens , A. J. Bray