• DOI:10.1007/s10955-021-02757-7
• Corpus ID: 222310436

Spherical Spin Glass Model with External Field

@article{Baik2020SphericalSG,
  title={Spherical Spin Glass Model with External Field},
  author={Jinho Baik and Elizabeth Collins-Woodfin and Pierre le Doussal and Hao Wu},
  journal={arXiv: Disordered Systems and Neural Networks},
  year={2020}
}

• J. Baik, Elizabeth Collins-Woodfin, +1 author Hao Wu
• Published 13 October 2020
• Physics
• arXiv: Disordered Systems and Neural Networks

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.