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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.15664 |
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| _version_ | 1866914339020079104 |
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| author | Shen, Mutian Xu, Yichen Nussinov, Zohar |
| author_facet | Shen, Mutian Xu, Yichen Nussinov, Zohar |
| contents | We introduce the Eggbox Ising model, a tunable construction of rugged energy landscapes defined by distances to a prescribed set of patterns. Correlated pattern ensembles realize arbitrary k-step replica-symmetry-breaking structures and controllable Parisi overlap distributions p(q), consistent with the hierarchical overlap structure observed in a simple word-embedding example from empirical data. A softened variant allows a systematic expansion leading to Hopfield-type couplings (and higher-body terms). We analyze the density of states and show that suitable potentials induce discontinuous finite-temperature transitions with metastability and hysteresis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Eggbox Ising Model Shen, Mutian Xu, Yichen Nussinov, Zohar Statistical Mechanics Computational Physics We introduce the Eggbox Ising model, a tunable construction of rugged energy landscapes defined by distances to a prescribed set of patterns. Correlated pattern ensembles realize arbitrary k-step replica-symmetry-breaking structures and controllable Parisi overlap distributions p(q), consistent with the hierarchical overlap structure observed in a simple word-embedding example from empirical data. A softened variant allows a systematic expansion leading to Hopfield-type couplings (and higher-body terms). We analyze the density of states and show that suitable potentials induce discontinuous finite-temperature transitions with metastability and hysteresis. |
| title | The Eggbox Ising Model |
| topic | Statistical Mechanics Computational Physics |
| url | https://arxiv.org/abs/2502.15664 |