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Updated: Aug 1, 2026
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Relation between coupled map lattices and kinetic ising models
1Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, D-01187 Dresden, Germany.
Summary
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.
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.
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