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Relation between coupled map lattices and kinetic ising models

Schmuser1, Just, Kantz

  • 1Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, D-01187 Dresden, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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This study introduces a new coupled map lattice model with symmetries similar to the Miller-Huse model. It reveals four distinct phases with unique ergodic behaviors and establishes an equivalence to kinetic Ising models.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Nonlinear Dynamics

Background:

  • Coupled map lattices (CMLs) are used to model complex spatio-temporal phenomena.
  • The Miller-Huse model is a significant benchmark in CML research.
  • Understanding phase transitions and ergodic behavior is crucial in nonlinear systems.

Purpose of the Study:

  • Introduce a novel one-dimensional coupled map lattice with specific symmetries.
  • Analyze its ergodic behavior and phase transitions.
  • Establish a connection between the CML and kinetic Ising models.

Main Methods:

  • Formal perturbation expansion with weak coupling.
  • Analysis near a symmetry-breaking bifurcation point.
  • Coarse-graining to derive a master equation.

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Main Results:

  • Identified four distinct phases with varying ergodic properties.
  • Observed predominant antiferromagnetic ordering despite diffusive coupling.
  • Demonstrated an equivalence between the CML and a kinetic Ising model.

Conclusions:

  • The introduced CML exhibits rich dynamical behavior and phase transitions.
  • The mapping to a kinetic Ising model provides insights into system dynamics.
  • Transient behavior and phase transitions are dependent on system size.