平面伊辛晶格的通用模拟器
A universal emulator for planar Ising lattices
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中文总结 AI 辅助
介绍二维伊辛模型模拟器概念，构建方形和三角形模拟器，用单一转移矩阵及特定晶格二进制掩码获热力学量，应用于多种晶格，该构建可直接扩展到分形和无序伊辛模型。
中文摘要 AI 辅助
我们引入了二维伊辛模型的伊辛模拟器概念：平面、单位边长晶格可表示为单个主体晶格的位点或键稀释超胞，其费曼 - 弗多维琴科/卡克 - 沃德解一劳永逸地固定。我们构建了明确的方形和三角形模拟器，并表明单个转移矩阵，辅以特定晶格的二进制掩码，给出了铁磁和反铁磁耦合的所有感兴趣的热力学量。我们将该框架应用于所有十一种阿基米德晶格、所有二十种二维均匀晶格（其热力学在此首次获得）以及几种五边形晶格，并表明相同的构建直接扩展到分形和无序伊辛模型，而无需对底层机制进行修改。
英文摘要
We introduce the notion of an Ising emulator for two-dimensional Ising models: flat, unit-edge-length lattices can be represented as site- or bond-diluted supercells of a single host lattice, for which the Feynman--Vdovichenko/Kac--Ward solution is fixed once and for all. We construct explicit square and triangular emulators and show that a single transition matrix, supplemented by lattice-specific binary masks, gives all the thermodynamic quantities of interest for both ferro- and antiferromagnetic couplings. We apply the framework to all eleven Archimedean lattices, to all twenty $2$-uniform lattices -- whose thermodynamics is obtained here for the first time -- and to several pentagonal lattices, and show that the same construction extends directly to fractal and disordered Ising models, with no modification to the underlying machinery.
