Metric characterization of cluster dynamics on the Sierpinski gasket

Abstract

We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring on cellular automata defined on an arbitrary structure. As a prototype for such systems we focus on the Ising model on a finite Sierpsinski Gasket, which is known to possess a complex thermodynamic behavior. Our algorithm requires the projection of evolving configurations into an appropriate partition space, where an information-based metrics (Rohlin distance) can be naturally defined and worked out in order to detect the changing and the stable components of clusters. The analysis highlights the existence of different temperature regimes according to the size and the rate of change of clusters. Such regimes are, in turn, related to the correlation length and the emerging "critical" fluctuations, in agreement with previous thermodynamic analysis, hence providing a non-trivial geometric description of the peculiar critical-like behavior exhibited by the system. Moreover, at high temperatures, we highlight the existence of different time scales controlling the evolution towards chaos.

arXiv comment20 pages, 8 figures

References in corpus (8)

• The Shapes of Cooperatively Rearranging Regions in Glass Forming Liquids
• Phase-ordering kinetics on graphs
• Spontaneous magnetization of the Ising model on the Sierpinski carpet fractal, a rigorous result
• Lee-Yang zeros and the Ising model on the Sierpinski Gasket
• Configurations and Observables in an Ising Model with Heat Flow
• Generalization of the Peierls-Griffiths Theorem for the Ising Model on Graphs
• Metric Features of a Dipolar Model
• Energy Transport in an Ising Disordered Model

Cited by in corpus (2)

• Equilibrium statistical mechanics on correlated random graphs
• Slow relaxation in microcanonical warming of a Ising lattice