发表机构
KAIST（韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究软球Sherrington-Kirkpatrick模型，证明其自由能在高温区呈高斯涨落，低温区由最大特征值主导并收敛于GOE Tracy-Widom分布，表明软径向约束保留经典模型的涨落转变。
AI 中文摘要
我们考虑软版本的球面Sherrington-Kirkpatrick模型，其中球面约束被径向限制项所替代。我们证明，在适当的谱假设下，对于实对称无序矩阵，自由能表现出两种不同的涨落机制。在高温区域，涨落渐近服从高斯分布。在低温区域，涨落由最大特征值控制，并收敛于GOE Tracy-Widom分布。这些结果表明，软径向约束保留了经典球面Sherrington-Kirkpatrick模型的涨落转变。
英文摘要
We consider a soft version of the spherical Sherrington-Kirkpatrick model, where the spherical constraint is replaced by a radial confinement term. We prove that, for a real symmetric disorder matrix under suitable spectral assumptions, the free energy exhibits two distinct fluctuation regimes. In the high-temperature regime, the fluctuations are asymptotically Gaussian. In the low-temperature regime, the fluctuations are governed by the largest eigenvalue and converge to the GOE Tracy-Widom distribution. These results show that the soft radial constraint preserves the fluctuation transition of the classical spherical Sherrington-Kirkpatrick model.
