Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-10-15
Eur. Phys. J. B 44, 79-92 (2005)
Physics
Condensed Matter
Statistical Mechanics
28 pages, 8 figures
Scientific paper
10.1140/epjb/e2005-00102-y
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest' still holds in the mean-field limit, where the model exhibits glassy dynamics, with two well separated time scales, corresponding to individual and collective behaviour. The survival probability of a cluster eventually falls off according to the universal law $(\ln t)^{-1/2}$. Beyond mean field, the dynamics exhibits both aging and metastability, with a finite fraction of the clusters surviving forever and forming a non-trivial spatial pattern.
Luck Mck. J.
Mehta Anita
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