Dynamical universality classes of simple growth and lattice gas models

Jeffrey Kelling, G. Ódor, Sibylle Gemming

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson class for linear surface growth. The autocorrelation functions of the heights and the dimer lattice gas variables are determined with high precision. Parallel random-sequential (RS) and two-sub-lattice stochastic dynamics (SCA) have been compared. The latter causes a constant correlation in the long time limit, but after subtracting it one can find the same height functions as in case of RS. On the other hand the ordered update alters the dynamics of the lattice gas variables, by increasing (decreasing) the memory effects for nonlinear (linear) models with respect to RS. Additionally, we support the KPZ ansatz and the Kallabis-Krug conjecture in 2 + 1 dimensions and provide a precise growth exponent value β=0.2414(2). We show the emergence of finite size corrections, which occur long before the steady state roughness is reached.

Original languageEnglish
Article number035003
JournalJournal of Physics A: Mathematical and Theoretical
Volume51
Issue number3
DOIs
Publication statusPublished - Jan 19 2018

Fingerprint

Lattice Gas Model
Universality
Lattice Gas
Gases
Autocorrelation
gases
Dimers
Lattice Dynamics
Surface Growth
Octahedron
Memory Effect
Surface roughness
Stochastic Dynamics
Dimer
Autocorrelation Function
two dimensional models
Data storage equipment
Roughness
autocorrelation
Nonlinear Model

Keywords

  • Autocorrelation
  • Driven lattice gas
  • Edwards-Wilkinson class
  • Kardar- Parisi-Zhang class
  • Stochastic cellular automaton
  • Surface growth

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

Dynamical universality classes of simple growth and lattice gas models. / Kelling, Jeffrey; Ódor, G.; Gemming, Sibylle.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 51, No. 3, 035003, 19.01.2018.

Research output: Contribution to journalArticle

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