Colloquium: Tuesday, January 4, 2022. Speaker: Eliran Subag (Weizmann). Title: “Generalized TAP approach for spherical spin glasses”.
The last colloquium for this semester will be held ONLINE on 4.1.2022 at 14:00 (Tuesday).
Speaker: Eliran Subag (Weizmann)
Date: Tuesday, January 4, 2022
Title: Generalized TAP approach for spherical spin glasses
Abstract: Spherical spin glasses are certain random functions on the sphere in R^N. The fundamental problem in their study in physics — namely, computing the free energy — is equivalent to analyzing the volumes of their level sets as the dimension N tends to infinity. The solution to this problem was famously invented by G. Parisi, (originally for the SK model) who was recently awarded the Nobel Prize. Two and a half decades after its discovery, Parisi’s formula was rigorously proven by Guerra and Talagrand.
Another approach to analyze mean-field spin glass models was proposed in the 70s by Thouless, Anderson and Palmer (TAP). After reviewing the above, I will discuss recent developments in rigorously proving main ingredients from their approach, including a certain representation for the free energy. I will then explain how the free energy can be computed from the latter for the pure spherical models, and their so-called multi-species version for which an analogue of Parisi’s formula is not known.