The antiferromagnetic Ising model beyond line graphs

Mark Jerrum

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arXiv · 2602.14915

The antiferromagnetic Ising model beyond line graphs

Mark Jerrum

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Abstract

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.

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Mark Jerrum. 2026-02-16. The antiferromagnetic Ising model beyond line graphs. https://arxiv.org/abs/2602.14915

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