论文标题
在高温下没有外部场的SK模型的两个点函数
The Two Point Function of the SK Model without External Field at High Temperature
论文作者
论文摘要
我们表明，两个点相关矩阵$ \ textbf {m} =（\langleσ_iσ_j\ rangle）_ {1 \ leq I，j \ leq n} $ sherrington-kirkpatrick a sherrington-kirkpatrick型号具有零外部字段型 \ [\ lim_ {n \ to \ infty} \ | \ textbf {m} - （1+β^2 - β\ textbf {g}）^{ - 1} \ | _ {\ text {op}} = 0 \]，在整个高温$β<1 $中。在这里，$ \ textbf {g} $表示模型的GOE交互矩阵。
We show that the two point correlation matrix $ \textbf{M}= (\langle σ_i σ_j\rangle)_{1\leq i,j\leq N} $ of the Sherrington-Kirkpatrick model with zero external field satisfies \[ \lim_{N\to\infty} \| \textbf{M} - ( 1+β^2 - β\textbf{G})^{-1} \|_{\text{op}} =0 \] in probability, in the full high temperature regime $β< 1$. Here, $\textbf{G}$ denotes the GOE interaction matrix of the model.
