1 3 M ar 2 00 7 epl draft Effective surface - tension in the noise - reduced voter model Luca

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. The theory of phase-ordering kinetics [1] describes the scaling behavior of domain coarsening phenomena occurring in non-equilibrium statistical physics, with applications ranging from social sciences [2] to ecology [3]. The way in which a system orders starting from a disordered phase follows different paths depending on generic properties (e.g. symmetries, the type of interactions, etc.) that allow to identify specific universality classes of nonequilibrium phase-ordering dynamics. In particular, the important family of ‘kinetic Ising models’ with Z2-symmetry and no strict conservation of the order parameter displays two different ordering behaviors, depending on whether a surface tension exists or not. If this is the case (as in Glauber dynamics, for example), coarsening is curvature-driven [4]: the domain length scale grows following a power law, l(t) ∼ t in any dimension [1]. Other models, such as the voter model [5], exhibit domain coarsening without surface tension: dynamics is driven by interfacial noise [4]. In this case l(t) grows as t in one dimension, logarithmically in d = 2 and it does not diverge for d > 2 [6]. It is also possible to define a family of kinetic Ising models interpolating between zero-temperature Glauber dynamics (T0GD) and the voter model (VM) [4,7,8]: in these models, the transition rates depend on two parameters measuring the strength of bulk and interfacial noise. When bulk noise is present the coarsening is curvature-driven. When only interfacial noise exists, coarsening is voter-like for a