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A simple two dimensional model of a phase growing on a substrate is introduced. The model is characterized by an adsorption rate q, and a desorption rate p. It exhibits a wetting transition which may be viewed as an unbinding transition of…

Statistical Mechanics · Physics 2009-10-30 Haye Hinrichsen , Roberto Livi , David Mukamel , Antonio Politi

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behavior quite different from that of their equilibrium counterparts. Here we demonstrate a surprising…

Soft Condensed Matter · Physics 2016-08-09 Leiming Chen , Chiu Fan Lee , John Toner

Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…

Statistical Mechanics · Physics 2011-08-11 Kazumasa A. Takeuchi , Masaki Sano , Tomohiro Sasamoto , Herbert Spohn

Ballistic deposition is one of the many models of interface growth that are believed to be in the KPZ universality class, but have so far proved to be largely intractable mathematically. In this model, blocks of size one fall independently…

Probability · Mathematics 2022-05-19 Sourav Chatterjee

We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a…

Statistical Mechanics · Physics 2021-08-05 Guillaume Barraquand , Alexandre Krajenbrink , Pierre Le Doussal

The Markov dynamics of interlaced particle arrays, introduced by A. Borodin and P. Ferrari in arXiv:0811.0682, is a classical example of (2+1)-dimensional random growth model belonging to the so-called Anisotropic KPZ universality class. In…

Probability · Mathematics 2022-03-01 Vincent Lerouvillois , Fabio Lucio Toninelli

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the…

Statistical Mechanics · Physics 2007-05-23 M. Constantin , C. Dasgupta , P. Punyindu Chatraphorn , Satya N. Majumdar , S. Das Sarma

An unbounded one-dimensional solid-on-solid model with integer heights is studied. Unbounded here means that there is no a priori restrictions on the discret e gradient of the interface. The interaction Hamiltonian of the interface is given…

Probability · Mathematics 2010-10-11 Gustavo Posta

We continue to study a model of disordered interface growth in two dimensions. The interface is given by a height function on the sites of the one--dimensional integer lattice and grows in discrete time: (1) the height above the site $x$…

Probability · Mathematics 2007-05-23 Janko Gravner , Craig A. Tracy , Harold Widom

Dynamics under which a system of Ising spins relaxes to a stationary state with Bolzmann-Gibbs measure and which do not fulfil the condition of detailed balance are irreversible and asymmetric. We revisit the problem of the determination of…

Statistical Mechanics · Physics 2015-06-15 Claude Godreche

While the 1-point height distributions (HDs) and 2-point covariances of $(2+1)$ KPZ systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and…

Statistical Mechanics · Physics 2023-06-29 Ismael S. S. Carrasco , Tiago J. Oliveira

We investigate the evolution of the random interfaces in a two dimensional Potts model at zero temperature under Glauber dynamics for some particular initial conditions. We prove that under space-time diffusive scaling the shape of the…

Probability · Mathematics 2007-05-23 Glauco Valle

Until very recently, the asymptotic occurrence of intrinsic anomalous scaling has been expected to require concomitant effects for kinetically rough interfaces, like quenched disorder or morphological instabilities. However, counterexamples…

Statistical Mechanics · Physics 2024-05-15 E. Rodriguez-Fernandez , S. N. Santalla , M. Castro , R. Cuerno

To quantitatively characterize height distributions (HDs), one uses adimensional ratios of their first central moments ($m_n$) or cumulants ($\kappa_n$), especially the skewness $S$ and kurtosis $K$, whose accurate estimate demands an…

Statistical Mechanics · Physics 2022-06-24 Tiago J. Oliveira

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

Statistical Mechanics · Physics 2011-09-09 Guy Fayolle , Cyril Furtlehner

Building on an analogy between the ageing behaviour of magnetic systems and growing interfaces, the Arcetri model, a new exactly solvable model for growing interfaces is introduced, which shares many properties with the kinetic spherical…

Statistical Mechanics · Physics 2015-09-01 Malte Henkel , Xavier Durang

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of…

Statistical Mechanics · Physics 2015-06-03 M. O. Hase , M. J. de Oliveira

We investigate the behavior of discrete interface growth models belonging to the Edwards--Wilkinson (EW) and Kardar--Parisi--Zhang (KPZ) universality classes, when defined on a complete graph, a topology commonly used to probe the…

Statistical Mechanics · Physics 2026-05-01 J. M. Marcos , J. J. Meléndez , R. Cuerno , J. J. Ruiz-Lorenzo

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an…

Statistical Mechanics · Physics 2012-08-31 J. Ricardo G. Mendonça

The irreversible growth of a binary mixture under far-from-equilibrium conditions is studied in three-dimensional confined geometries of size $L_x \times L_y \times L_z$, where $L_z \gg L_x = L_y$ is the growing direction. A competing…

Statistical Mechanics · Physics 2009-11-11 Julián Candia , Ezequiel V. Albano