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Kinetic Ashkin-Teller model with competing dynamics.

S Bekhechi1, A Benyoussef, B Ettaki

  • 1Laboratoire de Magnétisme et de Physique des Hautes Energies, Département de Physique, Faculté des Sciences, Université Mohammed V, Avenue Ibn Battota, Boîte Postale 1014, Rabat, Morocco.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 20, 2001
PubMed
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This study explores a two-dimensional nonequilibrium Ashkin-Teller model using competing dynamics. Results show self-organization and preservation of equilibrium critical behavior under nonequilibrium conditions.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Investigating nonequilibrium systems is crucial for understanding complex phenomena beyond thermodynamic equilibrium.
  • The Ashkin-Teller model provides a framework for studying systems with competing interactions and multiple order parameters.
  • Nonequilibrium dynamics, driven by external energy flux, can lead to novel emergent behaviors.

Purpose of the Study:

  • To investigate the phase diagram and critical behavior of a two-dimensional nonequilibrium Ashkin-Teller model.
  • To understand the interplay between thermal fluctuations (Glauber dynamics) and energy flux (Kawasaki dynamics).
  • To identify self-organization phenomena and assess the preservation of equilibrium critical behavior under nonequilibrium conditions.

Main Methods:

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  • Utilizing Monte Carlo simulations to model the system's dynamics.
  • Implementing competing stochastic processes: Glauber dynamics (probability p) for heat bath contact and Kawasaki dynamics (probability 1-p) for energy flux.
  • Calculating critical exponents to characterize the phase transitions.

Main Results:

  • The phase diagrams exhibit a self-organization phenomenon for specific fourth coupling interaction strengths.
  • Exponent calculations indicate that equilibrium critical behavior is preserved even when nonequilibrium conditions are applied.
  • The model demonstrates complex stationary states arising from competing dynamics.

Conclusions:

  • The studied nonequilibrium Ashkin-Teller model displays rich phase behavior, including self-organization.
  • Despite the introduction of energy flux, the system's critical behavior remains consistent with equilibrium predictions.
  • This research contributes to the understanding of driven systems and their emergent properties.