Elizabeth W. Collins-Woodfin, University of Michigan
Authors: Jinho Baik, Elizabeth Collins-Woodfin, Pierre le Doussal, Hao Wu
2022 AWM Research Symposium
Women in Analysis Research Network - Special Session for Graduate Students and Postdoctoral Fellows

The focus of this talk will be the 2-spin spherical Sherrington Kirkpatrick (SSK) spin glass model with an external field. More specifically, I will discuss the transition between this model and the one without an external field. The talk will provide a brief introduction to the SSK model, focusing on the distribution of spins and how that distribution changes in the presence of an external field. I will then discuss the transitional case in which the strength of the external field goes to zero as the dimension of the spin variable grows. I will present results for the overlap with the external field and the overlap with the ground state, focusing on what each quantity tells us about the distribution of spins. Finally, I will provide a brief overview of our methods, including a contour integral representation of the partition function as well as random matrix techniques. This talk is based on joint work with Jinho Baik, Pierre le Doussal, and Hao Wu.

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