Abstract.
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.
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Luck, J., Mehta, A. A deterministic model of competitive cluster growth: glassy dynamics, metastability and pattern formation. Eur. Phys. J. B 44, 79–92 (2005). https://doi.org/10.1140/epjb/e2005-00102-y
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DOI: https://doi.org/10.1140/epjb/e2005-00102-y