Integrable Systems and Random Matrix Theory Seminar

This talk will focus on results from a recent preprint by Baik, Collins-Wildman, Le Doussal and Wu. In the preprint, we analyze the free energy and the overlaps in the 2-spin spherical Sherrington Kirkpatrick (SSK) spin glass model with an external field. Our goal is to understand the transition between this model and the one without an external field. My 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 overlaps with the external field, with the ground state and with a replica, focusing on what each of these overlaps 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. Speaker(s): Elizabeth Collins-Wildman (University of Michigan)