Title: Cluster expansion method in Spin glasses
Abstract: Cluster expansion approach was used in the seminal work of Aizenman-Lebowitz-Ruelle (1987) to understand the distributional limit of the free energy in the high-temperature SK spin glass model with zero external field. The main idea is to convert the probabilistic problem into a counting problem. We use this approach to understand the high-temperature behavior of a few Spin glass models, including
a) Sherrington Kirkpatrick Spin glass model under weak external field,
b) mixed p-spin glass model with zero and weak external field,
c) heavy-tailed p-spin glass under zero and weak external field.
Time permitting we will discuss application to mean-field traveling salesman, matching and spanning tree problems. Based on joint work with Qiang Wu and Greg Terlov.