Opinion inertia and coarsening in the Persistent Voter model

We consider the Persistent Voter model (PVM), a variant of the Voter model (VM) that includes transient, dynamically-induced zealots. Due to peer reinforcement, the internal confidence $\eta_i$ of a normal voter increases by steps of size $\Delta\eta$ and once it gets above a given threshold, it becomes a zealot. Then, its opinion remains frozen until enough interactions with the opposite opinion occur and its confidence is reset. No longer a zealot, the regular voter may change opinion once again. This opinion inertia mechanism, albeit simplified, is responsible for an effective surface tension and the PVM has a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, as in the Ising Model at low temperature (IM0). The average time $\tau$ to attain consensus is non-monotonic on $\Delta\eta$ and has a minimum at $\Delta\eta_{\min}$. In this paper we clarify the mechanisms that accelerate the system towards consensus close to $\Delta\eta_{\min}$. Close to the crossover at $\Delta\eta_{\min}$, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large and the surface tension, albeit small, is still enough to keep the shape and reduce the fragmentation of the domains. The large size of the AR in the region of $\Delta\eta_{\min}$ has two important effects that accelerates the dynamics. First, it dislodges the zealots in the bulk of the domains and second, it maximally suppresses the slowly-evolving stripes that normally form in Ising-like models. This suggests the importance of understanding the role of the AR, where the change of opinion is facilitated, and the interplay between regular voters and zealots when attempting to disrupt polarized states.