Spherical Spin Glass Model with External Field
Spherical Spin Glass Model with External Field
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DOI：
10.1007/s10955-021-02757-7
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发表时间：
2020-10
影响因子：
1.6
通讯作者：
J. Baik;Elizabeth Collins-Woodfin;P. Le Doussal;Hao Wu
中科院分区：
文献类型：
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作者：
J. Baik;Elizabeth Collins-Woodfin;P. Le Doussal;Hao Wu
本文分析了外场作用下的2-自旋球Sherrington柯克帕特里克自旋玻璃模型的自由能和重叠，以了解该模型与无外场模型之间的转变.我们计算的极限值和波动的自由能，以及三种类型的重叠的设置中的外部场的强度为零的自旋变量的尺寸的增长。特别是，我们考虑与外部场，基态和副本的重叠。我们的方法涉及的轮廓积分表示的分区函数沿着与随机矩阵技术。我们还提供了不同的缩放制度之间的匹配计算。最后，我们讨论了磁化率和吉布斯测度的几何我们的结果的影响。Landon和Sosoe在他们最近的独立和同时发表的论文中严格证实了本文的一些发现。
We analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick spin glass model with an external field for the purpose of understanding the transition between this model and the one without an external field. We compute the limiting values and fluctuations of the free energy as well as three types of overlaps in the setting where the strength of the external field goes to zero as the dimension of the spin variable grows. In particular, we consider overlaps with the external field, the ground state, and a replica. Our methods involve a contour integral representation of the partition function along with random matrix techniques. We also provide computations for the matching between different scaling regimes. Finally, we discuss the implications of our results for susceptibility and for the geometry of the Gibbs measure. Some of the findings of this paper are confirmed rigorously by Landon and Sosoe in their recent paper which came out independently and simultaneously.