持久选民模型中的意见惯性与粗化
Opinion inertia and coarsening in the Persistent Voter model
AI总结：
本文研究持久选民模型中的意见惯性机制，阐明了共识平均时间最短的Δη_min附近，大尺寸活性区通过移出畴内狂热者、抑制慢演化条纹加速共识的机制，为打破极化状态提供参考。
摘要：
我们研究了持久选民模型（Persistent Voter model, PVM），它是选民模型（Voter model, VM）的一种变体，包含由动态诱导的瞬时狂热者。在同伴强化作用下，普通选民的内部置信度$η_i$会以$Δη$为步长增长，一旦超过给定阈值，该选民就会转变为狂热者。此后其意见将保持冻结，直到与相反意见发生足够多的相互作用、置信度被重置为止。不再是狂热者的普通选民可以再次改变意见。这种意见惯性机制虽然经过简化，却能产生有效表面张力，且PVM存在动力学 crossover（转变）：从VM那样的涨落驱动动力学，转变为低温伊辛模型（Ising Model at low temperature, IM0）那样的曲率驱动动力学。达到共识的平均时间$τ$随$Δη$呈非单调变化，且在$Δη_{\text{min}}$处存在最小值。本文阐明了在$Δη_{\text{min}}$附近加速系统达成共识的机制。在接近$Δη_{\text{min}}$的转变点处，普通选民聚集的畴周围的中间区域（即活性区active region, AR）范围很大，此时表面张力虽小，但仍足以维持畴的形状并减少畴的碎片化。$Δη_{\text{min}}$区域内AR的大尺寸会产生两个加速动力学的重要效应：第一，它会将畴内部的狂热者移出；第二，它能最大程度抑制类伊辛模型中通常会形成的演化缓慢的条纹结构。这表明，若试图打破极化状态，理解意见转变更易发生的AR的作用，以及普通选民与狂热者之间的相互作用至关重要。
英文摘要：
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 $η_i$ of a normal voter increases by steps of size $Δη$ 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 $τ$ to attain consensus is non-monotonic on $Δη$ and has a minimum at $Δη_{\min}$. In this paper we clarify the mechanisms that accelerate the system towards consensus close to $Δη_{\min}$. Close to the crossover at $Δη_{\min}$, 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 $Δη_{\min}$ 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.
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