The Eggbox Ising Model

Mutian Shen; Yichen Xu; Zohar Nussinov

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arXiv · 2502.15664

The Eggbox Ising Model

Mutian Shen·Yichen Xu·Zohar Nussinov

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Abstract

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.

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Mutian Shen, Yichen Xu, Zohar Nussinov. 2025-02-21. The Eggbox Ising Model. https://arxiv.org/abs/2502.15664

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