We study the mean-field Ising spin glass model with external field, where the random symmetric couplings matrix is orthogonally invariant in law. For sufficiently high temperature, we prove that the replica-symmetric prediction is correct for the first-order limit of the free energy. Our analysis is an adaption of a "conditional quenched equals annealed" argument used by Bolthausen to analyze the high-temperature regime of the Sherrington-Kirkpatrick model. We condition on a sigma-field that is generated by the iterates of an Approximate Message Passing algorithm for solving the TAP equations in this model, whose rigorous state evolution was recently established.

中文翻译：

---

具有正交不变耦合的Ising自旋玻璃的复制对称自由能

我们研究了带有外场的均场伊辛旋转玻璃模型，其中随机对称耦合矩阵在法律上是正交不变的。对于足够高的温度，我们证明了复制对称预测对于自由能的一阶极限是正确的。我们的分析是对博尔特豪森用来分析Sherrington-Kirkpatrick模型的高温状态的“条件淬火等于退火”论证的改编。我们以由近似消息传递算法的迭代生成的sigma域为条件，该算法用于求解该模型中的TAP方程，该模型的严格状态演化最近得到了建立。