标题： 两自旋球面Sherrington-Kirkpatrick模型在任何温度下的自由能极限的简短证明 显示英文标题

标题： A short proof of free energy limit of two spin spherical Sherrington-Kirkpatrick model at any temperature

摘要： 在本文中，我们提供了一个关于无外场球面2自旋Sherrington-Kirkpatrick（SSK）模型自由能极限的简短证明。 该证明适用于所有温度，并基于积分的拉普拉斯方法以及对整个空间的离散近似。 该证明足够一般，可以适应任何特征值分布具有某些良好性质的相互作用矩阵。 高温情况下的证明与[BK19]中给出的证明相同。 然而，低温情况下的证明是新的。 显示英文摘要

摘要： In this paper, we present a short proof of the limit of free energy of spherical 2 spin Sherrington-Kirkpatrick (SSK) model without external field. This proof works for all temperatures and is based on the Laplace method of integration and considering a discrete approximation of the whole space. This proof is general enough and can be adapted to any interaction matrix where the eigenvalue distribution has some nice properties. The proof in the high-temperature case is the same as the proof given in [BK19]. However, the low-temperature case is new.