We discuss how to apply the dimer method to Ising models on group latticeshaving non trivial topological genus $g$. We find that the use of groupextension and the existence of both external and internal group isomorphismsgreatly reduces the number of distinct Pfaffians and leads to explicittopological formulas for their sign and weight in the expansion of thepartition function. The complete solution for the Ising model on the Kleinlattice group $L(2,7)$ with $g=3$ is given.
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机译：我们讨论如何在群晶格具有非平凡拓扑属$ g $的情况下将二聚体方法应用于Ising模型。我们发现组扩展的使用以及内部和外部组同构的存在极大地减少了不同的Pfaffian的数量，并为它们在分配功能扩展中的符号和权重得出了明确的拓扑公式。给出了Kleinlattice组$ L（2,7）$上$ g = 3 $的Ising模型的完整解。
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