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Dynamical model of Ising spins.

Katarzyna Sznajd-Weron¹

¹Institute of Theoretical Physics, University of Wrocław, pl. Maxa Borna 9, 50-204 Wrocław, Poland. kweron@ift.uni.wroc.pl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 5, 2004

Summary

This study introduces a 2D Ising spin model using a novel disagreement function to control dynamics. Local minimization paradoxically increases global disagreement, leading to multiple distinct steady states from identical initial conditions.

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Area of Science:

Statistical mechanics
Complex systems dynamics

Background:

Traditional Ising models rely on energy minimization.
Defining energy in certain dynamical systems presents challenges.

Purpose of the Study:

Introduce a novel dynamical model for two-dimensional Ising spins.
Investigate system dynamics using a disagreement function instead of energy.
Explore the emergence of multiple steady states from identical initial conditions.

Main Methods:

Developed a two-dimensional dynamical model of Ising spins.
Introduced and utilized a 'disagreement function' to guide spin dynamics.
Analyzed system behavior through local minimization of the disagreement function.
Mapped the system's phase diagram.

Main Results:

Local minimization of the disagreement function can unexpectedly increase its global value.
Demonstrated that identical initial conditions can result in diverse final steady states.
Presented a comprehensive phase diagram illustrating system behavior.

Conclusions:

The novel disagreement function effectively drives system dynamics in the absence of a defined energy function.
The model exhibits complex behavior, including sensitivity to initial conditions and multistability.
This approach offers a new perspective on modeling complex systems with non-energy-based dynamics.

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