带外场的 Sherrington--Kirkpatrick 模型中自旋协方差的极限定理

我们研究带外场的 Sherrington--Kirkpatrick 模型中两处位置自旋的协方差（关于 Gibbs 测度）；当模型的位置数趋于无穷时，对该协方差的 $p$ 阶矩进行渐近估计，可得到一个弱极限定理，其极限律一般为非高斯的。We study the covariance (for Gibbs measure) of spins at two sites in the case of a Sherrington--Kirkpatrick model with an external field. When the number of sites of the model grows to infinity, an asymptotic evaluation of the $p$ moments of that covariance allows us to obtain a weak limit theorem, with a generally non-Gaussian limit law.