Dynamics of opinion formation in the Voter model with long-range interactions

D. E. RODRIGUEZ; M. A. BAB; E. V. ALBANO

Pinamar, Argentina

Congreso; IV MEETING ON DYNAMICS OF SOCIAL AND ECONOMIC SYSTEMS; 2009

ASOCIACIÓN PARA EL ESTUDIO DE LA DINÁMICA DE LOS SISTEMAS SOCIO-ECONÓMICOS

In the Voter model each individual may have two states of opinion, and in an elementary dynamical step a randomly selected individual adopts the opinion of its nearest neighbor. In this way, the opinions could represent two candidates in a runoff election, buying-selling a product, Windows- Linux, PC-Mackintosh, etc. It is known that starting from a disorder state of opinion, the Voter model in Euclidian dimensions d<=2 tends to order in a well-defined state of opinion, i.e., one observes a coarsening process. In this work we report extensive Monte Carlo simulations of the onedimensional Voter model, but considering long-range interactions among individuals according to a probability given by P(r)=1/r(1+sigma), where sigma is a parameter and r is the distance between them. For the Voter model a standard order parameter (OP) to measure the ordering process is the density of nearest neighbors with different opinion. Our results indicate that the time evolution of the OP depends on the interaction range, i.e., sigma, as follows: i) for sigma< 1 one has that after a transient period, the OP assumes a stationary value (plateau) without reaching an ordered state, except for exponential decays due to finite-size effects. This behavior is similar to that observed for short-range interactions in d > 2, and in small-world networks; ii) for 1 <sigma < 4, the OP decays according to power laws with exponents dependent on sigma, reaching an absorbent ordered state; iii) for sigma > 4, the standard one-dimensional short-range behavior is recovered. The crossover between the sigma < 1 and sigma > 1 regimes is also discussed.