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Universality of (2+1)-dimensional restricted solid-on-solid models.

Jeffrey Kelling1,2, Géza Ódor3, Sibylle Gemming2,4

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This study shows that restricted solid-on-solid models exhibit Kardar-Parisi-Zhang surface growth scaling. Larger step heights increase scaling corrections, meaning smaller steps better represent long-wave scaling behavior.

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Area of Science:

  • Surface growth dynamics
  • Statistical physics
  • Computational modeling

Background:

  • The Kardar-Parisi-Zhang (KPZ) equation describes universal scaling in dynamic interfaces.
  • Understanding the behavior of restricted solid-on-solid (RSOS) models is crucial for validating theoretical models of surface growth.

Purpose of the Study:

  • To investigate the surface growth scaling behavior of RSOS models in D=2+1 dimensions.
  • To determine the influence of step heights (N) on the scaling properties.
  • To identify the optimal model parameters for capturing asymptotic scaling behavior.

Main Methods:

  • Extensive dynamical simulations using parallel multisurface algorithms.
  • Implementation of algorithms on graphics processing units (GPUs) for enhanced computational power.
  • Analysis of numerical data to identify scaling exponents and corrections to scaling.

Main Results:

  • RSOS models in D=2+1 dimensions demonstrate KPZ surface growth scaling.
  • Scaling behavior is observed irrespective of the step heights (N).
  • Corrections to scaling increase with increasing step heights (N).

Conclusions:

  • Smaller step-sized RSOS models provide a more accurate representation of asymptotic, long-wave scaling behavior.
  • The findings support the universality of KPZ scaling in various surface growth models.
  • Computational simulations on GPUs are effective for studying complex dynamical systems.