Proof of entropic order in Generalized Ising Models
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917400074518528 |
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| author | Andriolo, Enrico Nguyen, Mendel Richards, Emily Sulejmanpasic, Tin |
| author_facet | Andriolo, Enrico Nguyen, Mendel Richards, Emily Sulejmanpasic, Tin |
| contents | 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 $entropic$ $glass$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09768 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Proof of entropic order in Generalized Ising Models Andriolo, Enrico Nguyen, Mendel Richards, Emily Sulejmanpasic, Tin Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory 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 $entropic$ $glass$. |
| title | Proof of entropic order in Generalized Ising Models |
| topic | Statistical Mechanics High Energy Physics - Lattice High Energy Physics - Theory |
| url | https://arxiv.org/abs/2604.09768 |