平均场Ghatak-Sherrington模型的局域场极限定律
Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model
- University of Minnesota（明尼苏达大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对平均场Ghatak-Sherrington模型，运用腔方法与Sheng-Wu的重叠估计，证明非中心腔场的中心极限定理，确定局域场极限定律为高斯分布的随机有限混合，基于矩方法给出定量误差界。
AI中文摘要：
我们研究具有自旋值{0,±1,…,±S}的平均场Ghatak-Sherrington模型在高温区域的局域场极限定律。利用腔方法以及Sheng-Wu[SW24]的定量重叠与自重叠估计，我们证明了非中心腔场的中心极限定理，进而确定局域场极限定律为高斯分布的随机有限混合。该证明基于矩方法，并给出了定量误差界。
英文摘要：
We study the limiting law of local field in the mean field Ghatak-Sherrington model with spin values $\{0,\pm1,\ldots,\pm S\}$ in the high-temperature regime. Using the cavity method and the quantitative overlap and self-overlap estimates of Sheng-Wu~\cite{SW24}, we prove a central limit theorem for the non-centered cavity field. As a result, we then identify the local field limiting law as a random finite mixture of Gaussian distributions. The proof is based on moment method and gives a quantitative error bound.
