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arXiv · 2604.09768

Proof of entropic order in Generalized Ising Models

Enrico Andriolo·Mendel Nguyen·Emily Richards·Tin Sulejmanpasic
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Abstract

Ordering at arbitrarily high temperature - entropic order - has been argued to take place in a class of generalized Ising models parameterised by a real interaction parameter $p$ when $p\ge 1$. We give a rigorous proof of this conjecture. We further show that on arbitrary graphs, these models solve graph packing problems - crucially, the Maximum Independent Set optimisation problem. Due to the NP-hardness of this packing problem on generic graphs, some lattice systems will exhibit glassy phases. We call this phenomenon $entropic$ $glass$.

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Enrico Andriolo, Mendel Nguyen, Emily Richards, Tin Sulejmanpasic. 2026-04-10. Proof of entropic order in Generalized Ising Models. https://arxiv.org/abs/2604.09768

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