Anomalous lifetime distributions and topological traps in ordering dynamics

¹  IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), Campus Universitat Illes Balears E07122 Palma de Mallorca, Spain
²  Laboratory of Computational Engineering, Helsinki University of Technology - P.O. Box 9203, 02015 HUT, Finland

Received: 11 May 2007
Accepted: 31 July 2007

Abstract

We address the role of community structure of an interaction network in ordering dynamics, as well as associated forms of metastability. We consider the voter and AB model dynamics in a network model which mimics social interactions. The AB model includes an intermediate state between the two excluding options of the voter model. For the voter model we find dynamical metastable disordered states with a characteristic mean lifetime. However, for the AB dynamics we find a power law distribution of the lifetime of metastable states, so that the mean lifetime is not representative of the dynamics. These trapped metastable states, which can order at all time scales, originate in the mesoscopic network structure.