Dynamic behavior of the voter model on fractals: logarithmic-periodic oscillations as a signatura of time discrete scale invariante.

M BAB,; EZEQUIEL 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 the upper critical dimension (d < 2) and starting from a disordered configuration, a critical coarsening process takes place, and the density of interfaces, , decays as a power-law function of time. Recently published numerical studies performed on low-dimensional fractal substrates (dF < 2) [Physica A 362, 338 (2006)] show the existence of logarithmic-periodic oscillations superimposed on the standard 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. PACS 05.50.+q - Lattice theory and statistics. 64.60.Ht - Dynamic critical phenomena. 75.70.-i - Magnetic properties of thin films, surfaces, and interfaces. 05.10.Ln - Monte Carlo methods.