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.
@article{arxiv.2412.18070,
title = {On the occupancy fraction of the antiferromagnetic Ising model},
author = {Ewan Davies and Olivia LeBlanc},
journal= {arXiv preprint arXiv:2412.18070},
year = {2024}
}