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Kardar-Parisi-Zhang universality class and the anchored Toom interface.

G T Barkema1, P L Ferrari2, J L Lebowitz3

  • 1Institute for Theoretical Physics, Universiteit Utrecht, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands and Instituut-Lorentz, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands.

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Interface fluctuations in the anchored Toom model follow the Airy1 process, with space and time swapped. Numerical simulations confirm predictions from Kardar-Parisi-Zhang scaling theory, matching Tracy-Widom distributions.

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Area of Science:

  • Statistical Physics
  • Condensed Matter Physics
  • Nonlinear Dynamics

Background:

  • The anchored Toom interface is a model system for studying interface dynamics.
  • Kardar-Parisi-Zhang (KPZ) scaling theory describes universal properties of growing interfaces.

Purpose of the Study:

  • To investigate the statistical properties of interface fluctuations in the anchored Toom model.
  • To connect these fluctuations to established theoretical frameworks like KPZ theory and random matrix theory.

Main Methods:

  • Revisiting the anchored Toom interface model.
  • Applying Kardar-Parisi-Zhang (KPZ) scaling theory.
  • Numerical simulations to compute space-time statistics.
  • Comparison with Tracy-Widom distributions from random matrix theory.

Main Results:

  • Interface fluctuations are governed by the Airy1 process with interchanged space and time roles.
  • Numerical predictions for space-time statistics in the stationary state are well confirmed.
  • Spatial fluctuations agree with the GOE (Gaussian Orthogonal Ensemble) edge distribution.

Conclusions:

  • The Airy1 process provides a parameter-free description of anchored Toom interface fluctuations.
  • KPZ theory and random matrix theory offer a consistent framework for understanding these systems.
  • Numerical results validate the theoretical predictions for interface dynamics.