Latoski Luís Carlos F, Dantas W G, Arenzon Jeferson J
Instituto de Física, Universidade Federal do Rio Grande do Sul, CEP 91501-970, Porto Alegre - RS, Brazil.
Departamento de Ciências Exatas, EEIMVR, Universidade Federal Fluminense, CEP 27255-125, Volta Redonda - RJ, Brazil.
Phys Rev E. 2024 May;109(5-1):054115. doi: 10.1103/PhysRevE.109.054115.
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 in steps of size Δη. Once it surpasses a given threshold, it becomes a zealot. Its opinion remains frozen until enough interactions with the opposing opinion occur, resetting its confidence. No longer a zealot, the regular voter may change opinion once again. This mechanism of opinion inertia, though simplified, is responsible for an effective surface tension, and the PVM exhibits a crossover from a fluctuation-driven dynamics, as in the VM, to a curvature-driven one, akin to the Ising model at low temperature. The average time τ to attain consensus is nonmonotonic with respect to Δη and reaches a minimum at Δη_{min}. In this paper we elucidate the mechanisms that accelerate the system towards consensus close to Δη_{min}. Near the crossover at Δη_{min}, the intermediate region around the domains where the regular voters accumulate (the active region, AR) is large. The surface tension, albeit small, is sufficient to maintain the shape and reduce the domain fragmentation. The large size of the AR in the region of Δη_{min} has two important effects that accelerate the dynamics. First, it dislodges the zealots within the bulk of the domains. Secondly, it maximally suppresses the formation of slowly evolving stripes typical in Ising-like models. This suggests the importance of understanding the role of the AR, where opinion changes are facilitated, and the interplay between regular voters and zealots in disrupting polarized states.
我们考虑持久选民模型（PVM），它是选民模型（VM）的一种变体，其中包括瞬态的、动态诱导的狂热者。由于同伴强化，普通选民的内部信心η_i以大小为Δη的步长增加。一旦超过给定阈值，它就会变成一个狂热者。其观点保持不变，直到与相反观点发生足够多的相互作用，从而重置其信心。不再是狂热者后，普通选民可能会再次改变观点。这种观点惯性机制虽然简化，但会产生有效的表面张力，并且PVM表现出从波动驱动动力学（如VM中那样）到曲率驱动动力学的转变，类似于低温下的伊辛模型。达成共识的平均时间τ相对于 Δη 是非单调的，并在 Δη_min 处达到最小值。在本文中，我们阐明了在接近 Δη_min 时加速系统达成共识的机制。在 Δη_min 附近的交叉点处，普通选民聚集的区域（活跃区域，AR）周围的中间区域很大。表面张力虽然小，但足以维持形状并减少畴的碎片化。在 Δη_min 区域中 AR 的大尺寸有两个加速动力学的重要作用。首先，它将畴主体内的狂热者驱离。其次，它最大程度地抑制了类伊辛模型中典型的缓慢演化条纹的形成。这表明理解 AR 的作用以及普通选民和狂热者在破坏极化状态中的相互作用的重要性，在 AR 中观点变化更容易发生。
