Advisor: Michael Cranston

Abstract:

The main objective in spin glasses from the physical prospective is to
understand the strange magnetic properties of certain alloys. Yet the
models invented to explain the observed phenomena are also of a rather
fundamental nature in mathematics. In this talk, we will first introduce
the famous Sherrington-Kirkpatrick model as well as some known results
about this model such as the Parisi formula and the limiting behavior of
the Gibbs measure. Next, we will discuss the problems of chaos in the
mixed p-spin models and present mathematically rigorous results including
disorder, external field, and temperature chaos.