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This paper presents a significant theoretical advancement in classical statistical mechanics by constructing a 2D spin model with metastable states that remain stable under arbitrary Hamiltonian perturbations at non-zero temperatures. The authors achieve this rigorous result using recursive cluster expansions, offering new insights into the stability of complex energy landscapes relevant to optimization and sampling problems.

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A thermally and perturbatively stable classical spin model in two dimensions

arXiv19 octombrie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2610.22548v1 Announce Type: new Abstract: We show that the 2D classical spin model constructed in arXiv:2605.10943 hosts many metastable states at non-zero temperature which are stable to arbitrary Hamiltonian perturbations, providing the first such example. Our proof relies on a recursive application of the cluster expansion.

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