Chaotic Behavior and Damage Spreading in the Glauber Ising Model: A Master Equation Approach
We investigate the sensitivity of the time evolution of a kinetic Ising model with Glauber dynamics against the initial conditions. To do so we apply the "damage spreading" method, i.e., we study the simultaneous evolution of two identical systems subjected to the same thermal noise. We derive a master equation for the joint probability distribution of the two systems. We then solve this master equation within an effective-field approximation which goes beyond the usual mean-field approximation by retaining the fluctuations though in a quite simplistic manner. The resulting effective-field theory is applied to different physical situations. It is used to analyze the fixed points of the master equation and their stability and to identify regular and chaotic phases of the Glauber Ising model. We also discuss the relation of our results to directed percolation.
T. Vojta, "Chaotic Behavior and Damage Spreading in the Glauber Ising Model: A Master Equation Approach," Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, vol. 55, no. 5 A, pp. 5157-5164, American Physical Society (APS), May 1997.
The definitive version is available at https://doi.org/10.1103/PhysRevE.55.5157
Keywords and Phrases
Approximation theory; Chaos theory; Ferromagnetism; Magnetic fields; Mathematical models; Paramagnetism; Probability; Thermal noise; Thermodynamics; Damage spreading; Effective field theory; Glauber Ising model; Mean field approximation; Phase transitions
International Standard Serial Number (ISSN)
Article - Journal
© 1997 American Physical Society (APS), All rights reserved.