Both the antiferromagnetic Ising model and the hard-core model could be said to be tractable on line graphs of bounded degree. For example, Glauber dynamics is rapidly mixing in both cases. In the case of the hard-core model, we know that tractability extends further, to claw-free graphs and somewhat beyond. In contrast, it is shown here that the corresponding extensions are not possible in the case of the antiferromagnetic Ising model.

翻译：反对称伊辛模型与硬核模型均可视为在有界线图上可处理的模型。例如，在这两种情况下，Glauber动力学均呈现快速混合特性。对于硬核模型，已知其可处理性可进一步扩展至无爪图及稍更广泛的图类。相比之下，本文证明在反对称伊辛模型的情形下，相应的扩展是不可能的。