Eur. Phys. J. B 44, 79-92 (2005)
https://doi.org/10.1140/epjb/e2005-00102-y

A deterministic model of competitive cluster growth: glassy dynamics, metastability and pattern formation

¹ Service de Physique Théorique (URA 2306 of CNRS) , CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
² S.N. Bose National Centre for Basic Sciences, Block JD, Sector 3, Salt Lake, Calcutta 700098, India

Corresponding authors: ^a luck@spht.saclay.cea.fr - ^b anita@boson.bose.res.in

Received: 15 October 2004
Published online: 16 April 2005

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 . 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.