INIFTA   05425
INSTITUTO DE INVESTIGACIONES FISICO-QUIMICAS TEORICAS Y APLICADAS
Unidad Ejecutora - UE
artículos
Título:
Effective multidimensional crossover behavior in a one-dimensional voter model with long-range probabilistic interactions
Autor/es:
D. E. RODRIGUEZ; M. A. BAB; E. V. ALBANO
Revista:
PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS
Editorial:
American Physical Society
Referencias:
Año: 2010 vol. 83 p. 111101 - 1111010
ISSN:
1063-651X
Resumen:
A variant of the standard voter model, where a randomly selected site of a one-dimensional lattice (d=1) adopts the state of another site placed at a distance r from the previous one, is proposed and studied by means of numerical simulations that are rationalized with the aid of dynamical and finite-size scaling arguments. The distance between the two sites is also selected randomly with a probability given byP(r) \prop r^[-(d+\sigma)], where sigma is a control parameter. In this way one can study how the introduction of these long-range interactions influences the dynamic behavior of the standard voter model with nearest-neighbor interactions. It is found that the dynamics strongly depends on the range of the interactions, which is parameterized by sigma, leading to an interesting effective multidimensional crossover behavior, as follows. (a) For sigma<1 ordering is no longer observed and the average interface density \ro(t) assumes a steady state in the thermodynamic limit. Instead, for finite-size systems an exponential decay with a characteristic time (\tau) that increases with the size is observed. This behavior resembles the scenario corresponding to the short-range voter model for d>2, as well as the case of both scale-freeand small-world networks. (b) For sigma > 1, an ordering dynamics is observed, such that ro(t)\prop t^(-\alpha), where the exponent \alpha increases with \sigma until it reaches the value \alpha = 1/2 for \sigma >= 5, which corresponds to the behavior of  the standard voter model with short-range interactions in d = 1. (c) Finally, for \sigma=1 we show evidence of a critical-type behavior as in the case of the critical dimension (dc = 2) of the standard voter model.