Coarsening in the long-range Persistent Voter Model

Abstract

We investigate the coarsening kinetics in a long-range variant of the Persistent Voter Model in space dimensions $d=1$ and 2. In this model, agents can hold two confidence levels, normal and zealot. Normal agents imitate another opinion chosen at a distance $r$ with probability $P(r) \propto r^{-\alpha}$, with $\alpha >d$. On the contrary, while in the zealot state, agents keep their own opinion. Normal (zealot) agents can become zealots (normal) if their opinion is equal (different) to that of the chosen neighbour. Through numerical simulations we show that, for any values of $\alpha$, the model belongs to the same universality class of the long-range Ising model quenched to a small (non-zero) temperature, similarly to what was already known for the nearest-neighbor case. For the one-dimensional case, we further develop an analytical treatment, which reproduces the $\alpha$-dependence of the correlation length and the functional form of the correlation function. These results not only confirm that the introduction of opinion inertia mitigates the strong interfacial noise present in the Voter model, thus reinstating the basic kinetic mechanism of the Ising model, but also expand the applicability of this correspondence.