Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2010-09-12
J. Stat. Mech. (2010) P09002
Physics
Condensed Matter
Statistical Mechanics
20 pages, 8 figures
Scientific paper
10.1088/1742-5468/2010/09/P09002
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.
Agliari Elena
Casartelli Mario
Vivo Edoardo
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