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Dynamical phase transitions in cluster growth processes where growth sites have a finite lifetime

Journal of Physics A: General Physics, ISSN: 0305-4470, Vol: 21, Issue: 6, Page: L345-L351
1988
  • 10
    Citations
  • 0
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  • 1
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Metrics Details

  • Citations
    10
    • Citation Indexes
      10
  • Captures
    1

Article Description

The authors discuss variants of the Eden model for cluster growth, where growth sites have a finite lifetime tau . Time is increased by 1/G when a growth site is transformed into a cluster site; G is the total number of growth sites present at that time. They find by Monte Carlo simulation that the growth process depends drastically on tau . Below a critical lifetime tau ( tau approximately=0.80 on the square lattice) the clusters are described by the fractal dimension of self-avoiding random walks, d =4/3, and the number of cluster sites s increases proportional to time t. Above tau , one finds Eden clusters with d=2 and s approximately=t. Finally, the authors extend results to inhomogeneous media (percolation systems) where a fraction (1-p) of sites is not accessible to the growth process, and discuss the phase diagram.

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