Dynamic Behavoiur of the Voter Model on Fractals: Log-periodic Oscillations as a Signature of Time Discrete Scale Invariance

M. A. BAB; E. V. ALBANO

EUROPEAN PHYSICAL JOURNAL B - CONDENSED MATTER

EDP Sciences

Lugar: Paris; Año: 2008 vol. 63 p. 521 - 528

1434-6028

The understanding of the dynamic behavior of the voter model, in low-dimensional media, is a very interesting open topic. In fact, due to the absence of the interfacial tension, only the interfacial noise becomes relevant during the coarsening processes, bringing the possibility of studing a new physical process. In this way, it is known that below of upper critical dimension (d<2) and starting from a disordered configuration, a critical coarsening  process takes place, and the density of interfaces, ho(t), decays as a power-law function of time.  Recently published numerical studies performed on low-dimensional fractal substrates (d_{F}<2) (Suchecki K. and Holyst J. A., Physica A, {362}:338 (2006)) show the existence of logarithmic-periodic oscillations superimposed on the standard ho(t) power-law behavior, but the origin of those oscillations remains unclear. In this work, we provide an explanation of these oscillations in terms of  the interplay between the dynamics of the voter model and the discrete scale invariance of the underlying fractal substrate. Our arguments are verified by means of extensive numerical simulations carried out on different fractal substrates.