Statistical Mechanics, Analysis, and Probability
Course at Universität Heidelberg
Institut für Theoretische Physik
Most interesting models of Statistical Mechanics
cannot be solved in closed form. Nevertheless,
much useful, precise information can be gained using
relatively elementary, but mathematically rigorous,
methods. This course is to provide an introduction
to these methods and results, as well as a perspective on mathematical
structures that arise in that context.
Topics will include
A bird's eye view of statistical mechanics
Precise formulation of the main questions,
DLR equations, mean-field theory
The transfer matrix,
the two-dimensional Ising model,
and the Perron-Frobenius theorem
The Griffiths-Peierls argument
Cluster expansions and analyticity
Zeroes of partition functions, Yang-Lee theory,
the theory of Penrose and Lebowitz.
O(N)-models, quantum spin systems.
The Mermin-Wagner Theorem.
The infrared bound and continuous symmetry breaking.
Connections to large-deviation theory.
Analysis and Linear Algebra.
Basic ideas of classical and quantum mechanics.
Previous exposure to ideas of statistical mechanics
(e.g. in MKTP1) is helpful,
but not necessary to follow this course.
will be announced in class
||Tuesdays and Thursdays, 11:15-13:00
||Kleiner Hörsaal, Philosophenweg 12
||October 15, 2013