发表机构
Universidade Federal Fluminense; University of Augsburg（弗鲁米嫩塞联邦大学; 奥格斯堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文直接处理临界横场伊辛链的香农熵奇点，通过独立伯努利边表示Born分布，得到解析层级并闭式求值关键系数，验证了周期常数和区间系数。
AI 中文摘要
临界波函数的局部基香农熵包含普适的次主导信息，但临界横场伊辛链的香农点在传统Rényi方法中是奇异的。我们通过将完整的计算基Born分布表示为独立长程伯努利边的奇数次边界，直接在$n=1$处处理该问题。香农链式法则将熵分解为显式的独立边项和条件圈空间项。对于周期链，这分离出解析的边异常，并通过链接顶点支撑组织剩余常数。在所述有限部分匹配和森林假设下，每个非零链接系数均由显式的有限维积分表示，给出全阶解析层级；四顶点项以闭式形式求值，前几个链接扇区已几乎饱和已确立的周期常数，该常数也从精确的有限尺寸分布独立重建。对于区间，外部精确约化为一个幽灵顶点，显式的平方对数相互抵消，留下解析的边贡献$\gamma_E=\log2/4-1/16$。条件圈项具有精确的全支撑分解，分为物理线和幽灵链接扇区；在边界森林减除闭合的假设下，这些扇区为剩余对数系数定义全阶重整化线和单体-二聚体边界周期的层级。第一个完整增广链接系数以闭式形式求值，其线和幽灵边界层异常之间存在精确抵消；从精确有限尺寸概率的独立重建恢复了已确立的系数$\gamma_1=0.060020(3)$。
英文摘要
Local-basis Shannon entropies of critical wave functions contain universal subleading information, but the Shannon point of the critical transverse-field Ising chain is singular in the conventional Rényi approach. We treat it directly at $n=1$ by representing the complete computational-basis Born distribution as the odd-degree boundary of independent long-range Bernoulli edges. The Shannon chain rule separates the entropy into explicit independent-edge and conditional cycle-space terms. For the periodic chain this isolates the analytic edge anomaly and organizes the remaining constant by linked vertex support. Conditional on the stated finite-part matching and forest assumptions, every nonvanishing linked coefficient is represented by an explicit finite-dimensional integral, giving an all-orders analytic hierarchy; the four-vertex term is evaluated in closed form, and the first few linked sectors already nearly saturate the established periodic constant, which is also reconstructed independently from the exact finite-size distribution. For an interval, the exterior reduces exactly to one ghost vertex and the explicit squared logarithms cancel, leaving the analytic edge contribution $γ_E=\log2/4-1/16$. The conditional cycle term has an exact all-support decomposition into physical-line and ghost-linked sectors; conditional on closure of the boundary forest subtraction, these sectors define an all-orders hierarchy of renormalized line and monomer--dimer boundary periods for the remaining logarithmic coefficient. The first complete augmented linked coefficient is evaluated in closed form, with an exact cancellation between its line and ghost boundary-layer anomalies; an independent reconstruction from exact finite-size probabilities recovers the established coefficient $γ_1=0.060020(3)$.
Comments86 pages 5 figures
