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We study the Restricted Solid on Solid model for surface growth in spatial dimension $d=2$ by means of a multi-surface coding technique that allows to produce a large number of samples of samples in the stationary regime in a reasonable…

Disordered Systems and Neural Networks · Physics 2016-11-28 Andrea Pagnani , Giorgio Parisi

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes…

Statistical Mechanics · Physics 2014-11-24 Sidiney G. Alves , Tiago J. Oliveira , Silvio C. Ferreira

The natural paramterization or length for the Schramm-Loewner evolution (SLE{\kappa}) is the candidate for the scaling limit of the length of discrete curves for \kappa < 8. We improve the proof of the existence of the parametrization and…

Probability · Mathematics 2012-09-13 Gregory F. Lawler , Mohammad A. Rezaei

We present large-scale simulations of radial Eden clusters in three-dimensions and show that the growth exponent is in agreement with the value $\beta=0.242$ accepted for the Kardar-Parisi-Zhang (KPZ) universality class. Our results refute…

Statistical Mechanics · Physics 2012-10-26 Sidiney G. Alves , Silvio C. Ferreira

Amorphous solids may resist external deformation such as shear or compression while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid,…

Statistical Mechanics · Physics 2024-01-10 Nina Javerzat

We numerically test the correspondence between the scaling limit of self-avoiding walks (SAW) in the plane and Schramm-Loewner evolution (SLE) with k=8/3. We introduce a discrete-time process approximating SLE in the exterior of the unit…

Statistical Mechanics · Physics 2015-05-13 Marco Gherardi

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in d=2+1 by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different…

Statistical Mechanics · Physics 2013-04-23 Tiago J. Oliveira , Sidiney G. Alves , Silvio C. Ferreira

Motivated by the fact that many physical landscapes are characterized by long-range height-height correlations that are quantified by the Hurst exponent H, we investigate the statistical properties of the iso-height lines of correlated…

Statistical Mechanics · Physics 2018-08-27 Caio P. de Castro , Mirko Lukovic , Giacomo Pompanin , Roberto F. S. Andrade , Hans J. Herrmann

A series of recent works focused on two-dimensional interface growth models in the so-called Anisotropic KPZ (AKPZ) universality class, that have a large-scale behavior similar to that of the Edwards-Wilkinson equation. In agreement with…

Mathematical Physics · Physics 2020-09-29 Alexei Borodin , Fabio Lucio Toninelli

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with…

Statistical Mechanics · Physics 2009-11-07 Anna Chame , Fabio D. A. Aarao Reis

The Schramm-Loewner evolution (SLE_\kappa) is a candidate for the scaling limit of random curves arising in two-dimensional critical phenomena. When \kappa < 8, an instance of SLE_\kappa is a random planar curve with almost sure Hausdorff…

Probability · Mathematics 2009-06-23 Gregory F. Lawler , Scott Sheffield

We study a restricted solid-on-solid (RSOS) model involving deposition and evaporation with probabilities p and 1-p, respectively, in one-dimensional substrates. It presents a crossover from Edwards-Wilkinson (EW) to Kardar-Parisi-Zhang…

Statistical Mechanics · Physics 2014-05-07 T. J. Oliveira , K. Dechoum , J. A. Redinz , F. D. A. Aarao Reis

We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…

Statistical Mechanics · Physics 2014-12-23 I. S. S. Carrasco , K. A. Takeuchi , S. C. Ferreira , T. J. Oliveira

We show how to relate Schramm-Loewner Evolutions (SLE) to highest-weight representations of infinite dimensional Lie Algebras using the conformal restriction properties studied by Lawler, Schramm and Werner in the paper…

Mathematical Physics · Physics 2017-07-18 Roland Friedrich , Wendelin Werner

We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L= L_0 + \omega t^{\gamma}$. Our numerical simulations reveal that the competition between the substrate expansion and the…

Statistical Mechanics · Physics 2022-06-22 Ismael S. S. Carrasco , Tiago J. Oliveira

We introduce a self-organized surface growth model in 2+1 dimensions with anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative signs of…

Statistical Mechanics · Physics 2009-10-28 HaWoong Jeong , ByungNam Kahng , Doochul Kim

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 study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local…

Statistical Mechanics · Physics 2007-05-23 F. Hivert , S. Nechaev , G. Oshanin , O. Vasilyev

Real landscapes are usually characterized by long-range height-height correlations, which are quantified by the Hurst exponent $H$. We analyze the statistical properties of the isoheight lines for correlated landscapes of $H\in [-1,1]$. We…

Statistical Mechanics · Physics 2015-09-01 N. Pose , K. J. Schrenk , N. A. M. Araujo , H. J. Herrmann

We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height…

Statistical Mechanics · Physics 2009-10-28 M. Praehofer , H. Spohn