Metric Characterization of Cluster Dynamics on the Sierpinski Gasket Articles uri icon

authors

  • VIVO, EDOARDO
  • AGLIARI, E.
  • CASARTELLI, M.

publication date

  • September 2010

volume

  • 2010

International Standard Serial Number (ISSN)

  • 1742-5468

abstract

  • We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring for cellular automata defined on an arbitrary structure. As a prototype for such systems we
    focus on the Ising model on a finite Sierpinski 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 metric (the 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 timescales controlling the evolution towards
    chaos.