Effective surface-tension in the noise-reduced voter model

¹  Laboratoire de Physique Théorique (UMR du CNRS 8627) - Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France
²  Abdus Salam International center for Theoretical Physics - Strada Costiera 11, 34014, Trieste, Italy
³  Dipartimento di Fisica, Università “La Sapienza” and SMC-INFM - P.le A. Moro 2, 00185 Roma, Italy

Received: 7 December 2006
Accepted: 2 February 2007

Abstract

The role of memory is crucial in determining the properties of many dynamical processes in statistical physics. We show that the simple addition of memory, in the form of noise reduction, modifies the overall scaling behavior of the voter model, introducing an effective surface tension analogous to that recently observed in memory-based models of social dynamics. The numerical results for low-dimensional lattices show a scaling behavior in good agreement with usual Cahn-Allen curvature-driven coarsening, even though slower preasymptotic regimes may be observed depending on the memory properties. Simple arguments and a mean-field analysis provide an explanation for the observed behavior that clarifies the origin of surface tension and the mechanism underlying the coarsening process.