The Eggbox Ising Model
Statistical Mechanics
2026-02-20 v2 Computational Physics
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.
Cite
@article{arxiv.2502.15664,
title = {The Eggbox Ising Model},
author = {Mutian Shen and Yichen Xu and Zohar Nussinov},
journal= {arXiv preprint arXiv:2502.15664},
year = {2026}
}
Comments
14 pages, 12 figures