Papers › On the occupancy fraction of the antiferromagnetic Ising model

On the occupancy fraction of the antiferromagnetic Ising model

24 Dec 2024arXiv:2412.18070links table onlyarchive 2025-07-28

Ewan Davies, Olivia LeBlanc

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We study the maximum and minimum occupancy fraction of the antiferromagnetic Ising model in regular graphs. The minimizing problem is known to determine a computational threshold in the complexity of approximately sampling from the Ising model at a given magnetization, and our results determine this threshold for nearly the entire relevant parameter range in the case Δ=3. A small part of the parameter range lies outside the reach of our methods, and it seems challenging to extend our techniques to larger Δ.

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