Abstract

Spin glasses are disordered spin systems originated from the desire of understanding the strange magnetic behaviors of certain alloys in physics. As mathematical objects, they are often cited as examples of complex systems and have provided several fascinating structures and conjectures. In this talk, we will focus on the mixed p-spin model and discuss the ultrametric structure of its Gibbs measure. We will prove that this structure is indeed universal for any choice of the disorders under relevant moment matching assumptions. Based on joint work with A. Auffinger.