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 disordered models in detail. Examples include -
a) SK model under weak external field,
b) pure and mixed p-spin glass model with zero and weak external field,
c) heavy-tailed p-spin glass under zero and weak external field,
d) Potts spin glass model,
e) mean field traveling salesman, matching and spanning tree problems.
Based on joint work with Qiang Wu and Greg Terlov.