We show the equivalence of the 2D Ising model to standard free Euclidean lattice fermions of the Wilson Majorana type. The equality of the loop representations for the partition functions of both systems is established exactly for finite lattices with well-defined boundary conditions. The honeycomb lattice is particularly simple in this context and therefore discussed first and only then followed by the more familiar square lattice case.

中文翻译：

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Ising模型饰演Wilson-Majorana Fermions

我们展示了二维Ising模型与Wilson Majorana类型的标准自由欧几里得费米子的等效性。对于具有明确定义的边界条件的有限晶格，精确建立了两个系统的分区函数的循环表示的相等性。在这种情况下，蜂窝格特别简单，因此首先讨论，然后再讨论更熟悉的方格情况。