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Finite-size and finite-time scaling for kinetic rough interfaces.

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This study confirms that the dynamical structure factor uniquely characterizes interface dynamics. Finite-size and time scaling methods accurately establish universality classes for rough interfaces.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Kinetic rough interfaces exhibit space-time scale invariance.
  • Understanding the dynamics and universality classes of these interfaces is crucial.

Purpose of the Study:

  • To confirm that the dynamical structure factor uniquely characterizes interface dynamics.
  • To accurately establish universality classes for discrete interface models using scaling methods.

Main Methods:

  • Utilized the generic scaling theory by Ramasco et al.
  • Applied finite-size and finite-time scaling analyses.
  • Investigated self-organized interface models in random media with extremal dynamics.

Main Results:

  • The dynamical structure factor was confirmed as a unique dynamic characterizer.
  • Accurate estimation of critical exponents and scaling functions was achieved.
  • Isotropic and anisotropic interface models were analyzed, linking them to known universality classes.

Conclusions:

  • Finite-size scaling provides an alternative method for characterizing anomalous rough interfaces.
  • The isotropic model belongs to the same universality class as the Sneppen model (version A).
  • The anisotropic model is suggested to belong to the universality class of the tensionless Kardar-Parisi-Zhang (tKPZ) equation.