发表机构
Technische Universität Braunschweig; RWTH Aachen University; Utrecht University（布伦瑞克工业大学; 亚琛工业大学; 乌得勒支大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文数值研究二维阿贝尔沙堆模型的体关联函数，验证对数共形场论预测，并首次对kagome格进行系统数值分析，同时推导了高度-1概率的闭式解析表达式。
AI 中文摘要
我们数值研究了二维阿贝尔沙堆模型中的体关联函数，旨在既与对数共形场论的预测进行比较，又将分析扩展到难以应用解析方法的格点上。Wilson算法能够高效地并行生成大规模均匀生成树，这些生成树通过Majumdar--Dhar燃烧双射映射为独立的循环构型，从而消除了样本自相关并实现快速收敛。在方形（单子格）和蜂窝（双子格）格点上，我们的结果与分析预测吻合良好。对于kagome格，我们首次提供了体关联函数的系统性数值研究，并通过我们在此也利用格点格林函数推导出的闭式解析表达式，对体高度-1概率进行了交叉验证。
英文摘要
We numerically study the bulk correlation functions in the two-dimensional Abelian sandpile model, aiming both to compare with the predictions of logarithmic conformal field theory and to extend the analysis to lattices where analytical methods are difficult to apply. Wilson's algorithm efficiently generates large-scale uniform spanning trees in parallel, which can be mapped to independent recurrent configurations via the Majumdar--Dhar burning bijection, eliminating sample autocorrelations and yielding fast convergence. On the square (single-sublattice) and honeycomb (two-sublattice) lattices our results agree well with the analytical predictions. For the kagome lattice we provide the first systematic numerical study of the bulk correlation functions, and cross-check the bulk height-1 probability against a closed-form analytical expression that we also derive here via the lattice Green function.
