1996/11/28 by Thomas Vojta · 21 citations
Mathematics · Physics and Astronomy · #Chaotic #Complex Network Analysis Techniques #Computer science #Field (mathematics) #Glauber #Ising model #Master equation #Mathematics #Opinion Dynamics and Social Influence #Percolation (cognitive psychology) #Physics #Quantum mechanics #Stability (learning theory) #Statistical physics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.55.5157
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 55(5), 5157-5164 (American Physical Society) · 9 pages RevTeX, 4 EPS figures
arxiv created 1996/11/28 · openalex publication_date 1997/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.