Luca Smaldone — Università degli studi di Salerno #
Ordering kinetics of the voter model with long-range interactions #
We study, with analytical methods, the ordering kinetics of the long-range voter model. where agents on each vertex of a lattice take the opinion of another one at distance $r$ with probability $P(r) \propto r^{-\alpha}$. The model in $D$-dimensions exhibits different regimes, as $\alpha$ is varied. For $\alpha > D+2$, the behaviour is similar to that of the nearest-neighbor model. For $D <\alpha \leq D+2$, non-trivial stationary states appear even when $D<3$. Finally, for $\alpha \leq d$, the system behaves similarly as in the mean-field case.