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Spherical Spin Glass Model with External Field
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2021-05-07 , DOI: 10.1007/s10955-021-02757-7
Jinho Baik , Elizabeth Collins-Woodfin , Pierre Le Doussal , Hao Wu

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.



中文翻译:

带外场的球形自旋玻璃模型

我们分析带有外部场的2轴球形Sherrington Kirkpatrick自旋玻璃模型中的自由能和重叠,以了解该模型与没有外部场的模型之间的过渡。我们计算极限值和自由能的波动,以及在自旋变量的维数增大时外部场的强度变为零的情况下的三种重叠类型。特别地,我们考虑与外部场,基态和副本的重叠。我们的方法涉及分区函数的轮廓积分表示以及随机矩阵技术。我们还提供了不同缩放方式之间匹配的计算。最后,我们讨论了结果对磁化率和吉布斯量度的几何意义。

更新日期:2021-05-08
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