临界团簇递归中的涌现平衡结构
Emergent Equilibrium Structure Along a Critical Cluster Recursion
- University of Science and Technology of China（中国科学技术大学）
- Constructor University（Constructor 大学）
- Hefei National Laboratory, University of Science and Technology of China（合肥国家实验室，中国科学技术大学）
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China（中国科学院微观物理科学合肥国家研究中心和物理科学学院，中国科学技术大学）
- College of Physics, Guizhou University（贵州大学物理学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究在无固定耦合的临界团簇递归中，二维和三维下涌现出伊辛/FK相容条件结构，并通过精确因子分解识别出q=2的特殊性。
AI中文摘要：
临界普适性并不决定概率测度的微观条件结构。我们研究了一种双色团簇递归，该递归被约束在每一代都保持临界，且不施加平衡自旋测度或固定耦合。在二维和三维中，由此产生的依赖于历史的序列发展出共同的伊辛/福图因-卡斯泰莱因（FK）相容结构：单点条件律的第二壳层依赖性被强烈抑制，最近邻有效耦合逐渐向临界伊辛值附近靠拢，团簇和界面可观测量围绕相应的FK几何组织。一个精确的团簇着色因子分解将$q=2$单独挑出，作为残余连通权重从双色自旋边缘分布中消失的点。因此，平衡相容的条件结构可以沿着一条始终保持临界的轨迹涌现。
英文摘要：
Critical universality does not determine the microscopic conditional structure of a probability measure. We study a bicolored cluster recursion constrained to remain critical at every generation, with no equilibrium spin measure or fixed coupling imposed. In both two and three dimensions, the resulting history-dependent sequence develops a common Ising/Fortuin--Kasteleyn (FK) compatibility structure: the second-shell dependence of a one-site conditional law is strongly suppressed, nearest-neighbor effective couplings move progressively toward one another near the critical Ising value, and cluster and interface observables organize around the corresponding FK geometry. An exact cluster-coloring factorization singles out $q=2$ as the point where the residual connectivity weight disappears from the two-color spin marginal. Thus equilibrium-compatible conditional structure can emerge along a trajectory that remains critical throughout.
