多物种 SK 模型中具有中心高斯外场的德阿梅达-索利斯转变曲面
概率论
2025-11-25 v3 数学物理
math.MP
摘要
我们研究了具有中心高斯外场和半正定方差剖面矩阵的多物种 Sherrington-Kirkpatrick 模型中自由能 Parisi 公式的相变。我们证明，在外场强度和方差剖面的意义上，德阿梅达-索利斯曲面划定了 replica 对称解与 replica 对称破缺解之间的边界。
引用
@article{arxiv.2509.18066,
title = {On the de Almeida--Thouless Transition Surface in the Multi-Species SK Model with Centered Gaussian External Field},
author = {Heejune Kim},
journal= {arXiv preprint arXiv:2509.18066},
year = {2025}
}
备注
54 pages, 1 figure. Strengthened Proposition 3.1 to include external fields, revised Proposition 4.1 and the proof of the main theorem accordingly, and made minor revisions and updated acknowledgments