蛋盒伊辛模型
The Eggbox Ising Model
AI总结：
蛋盒伊辛模型通过可调的崎岖能量景观构造，实现了任意k步副本对称破缺结构，并展示了有限温度下的不连续相变特性。
摘要：
我们介绍了蛋盒伊辛模型，这是一种可调的崎岖能量景观构造，由到给定模式集的距离定义。相关模式集合实现了任意k步副本对称破缺结构和可控的帕拉西重叠分布p(q)，与从经验数据中观察到的简单词嵌入示例中的分层重叠结构一致。一种软化变体允许系统展开，导致霍普菲尔德型耦合（以及更高阶项）。我们分析了态密度，并表明合适的势能会引发在有限温度下的不连续相变，具有亚稳态和滞回现象。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
