abstract:
Lecture 1:
Overview of cluster expansions
Introduced to describe low-density or high-temperature systems, cluster
expansions have become the basic tool for rigorous perturbative arguments.
The first lecture will deal with the
following general issues:
(1) presentation of the general setting for hard-core systems;
(2) review of applications in statistical mechanics and probability theory,
and
(3) Penrose tree-graph identity.
additional material:
Find here
the slides of the lecture (1MB).
abstract:
The generalized random energy model (GREM)
is a simple spin glass model. However, several important aspects in spin
glass theory cannot be illuminated by this model, most notably
ultrametricity because the GREM is hierarchically constructed, and the chaos
property because the GREM does not have the chaos property predicted for the
SK-model. We propose some generalization of the GREM which hopefully shed
some light on these important open problems in spin glass theory.