标题： 透明世界中的集体通信：多体Potts模型中的相变和社会-量子对偶性 显示英文标题

标题： Collective communication in a transparent world: Phase transitions in a many-body Potts model and social-quantum duality

摘要： 我们考虑在高度透明的世界中，代理群体（“社区”）之间的“意见动态”所反映的类似谢尔灵的社会竞争。 具体而言，我们研究在一个完全图上具有竞争性二体和三体相互作用的$q$状态 Potts 自旋系统。 代理通过不同社区之间的成对排斥（对立意见）和同一社区内的三体吸引（共享意见）进行相互作用。 在热力学极限下，我们识别出三种关键相变的变体：(a) 一种对称的“混合”相，由$q$状态组成，在这种相中，社会中没有单一的意见占主导地位（被解释为“民主”），(b) 一种对称的“混合”相，但由$q-1$状态组成，以及 (c) 一种“共识”相，其特征是主导意见（或“意识形态”）的出现，并与对称分布的少数观点共存。 蒙特卡洛模拟揭示了有限尺寸效应和配置之间的亚稳态切换。 此外，我们将完全图上的社会模型与具有二次和三次相互作用的平均场$SU(N)$量子自旋系统建立了对应关系，揭示了一种“社会-量子”对偶性。 这种对偶性为社会交流的分层结构和量子多体现象提供了新的视角，为理解复杂系统中的涌现集体行为提供了一个统一的框架。 显示英文摘要

摘要： We consider the Schelling-like social competition reflected in "dynamics of opinions" among groups of agents ("communities") in a highly transparent world. Specifically, we investigate a $q$-state Potts spin system with competing two- and three-body interactions on a complete graph. Agents interact through pairwise repulsion (opposing opinions) between different communities and three-body attraction (shared opinions) within the same community. In the thermodynamic limit, we identify variants of three key phases: (a) a symmetric "mixed" phase of $q$ states, in which no single opinion dominates in the society (interpreted as a "democracy"), (b) a symmetric "mixed" phase but of $q-1$ states, and (c) a "consensus" phase, characterized by the emergence of a dominant opinion (or "ideology"), coexisting with symmetrically distributed minority views. Monte-Carlo simulations reveal finite-size effects and metastable switching between configurations. Furthermore, we establish a correspondence between our social model on a complete graph and the mean-field $SU(N)$ quantum spin system with both quadratic and cubic interactions, revealing a "social-quantum" duality. This duality provides new perspectives on both stratification of social communication, and quantum many-body phenomena, offering a unified framework for understanding emergent collective behavior in complex systems.