具有极端切换的二维BChS模型中的虚拟游走与相变
Virtual walks and phase transitions in two dimensional BChS model with extreme switches
AI总结：
本研究针对含极端态切换的二维扩展BChS观点形成模型，分析其对应的一维虚拟游走行为，通过有限尺寸标度法得到有序-无序相变，证实其临界性为Ising类并发现新的位移分布临界指数。
摘要：
我们研究了一维虚拟空间中的一种游走，该游走对应三态BChS观点形成模型的扩展版本——该模型最初发表于《Physica A》第391卷第3257页（2012年），其中智能体位于二维晶格上。观点取值为±1和0。本文中我们还考虑了极端态±1之间的切换。该模型包含两个噪声参数，分别代表负相互作用的比例p，以及表示极端切换概率的q。研究表明，当噪声参数超过特定阈值时，游走的性质会发生剧烈变化。我们利用有限尺寸标度法独立得到了有序-无序相变，结果显示这些阈值确实与存在相变的参数值一致。研究发现，即使允许极端切换，其临界行为仍属于Ising类。我们还得到了一个与位移概率分布相关的新临界指数，该指数与临界参数的取值无关。本文还将这类游走的性质与此前研究过的类似虚拟游走进行了比较。
英文摘要：
We have studied a walk in a one-dimensional virtual space corresponding to an extended version of the three-state BChS model of opinion formation, originally proposed in Physica A {\bf 391}, 3257 (2012), in which the agents are located on a two dimensional lattice. The opinions are designated by the values $\pm1$ and zero. Here we also consider switches between the extreme states $\pm 1$. The model involves two noise parameters representing the fraction of negative interactions $p$ and the probability of extreme switch denoted by $q$. The study shows that the nature of the walks changes drastically as the noise parameters exceed certain threshold values. The order-disorder phase transitions are independently obtained using the finite size scaling method showing that these threshold values are indeed consistent with those values of the parameters where a phase transition exists. The criticality is found to be Ising-like even when extreme switches are allowed. A new critical exponent associated with the probability distribution of the displacement is also obtained independent of the values of the critical parameters. The nature of the walks is compared to similar virtual walks studied earlier.
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