Statistical Mechanics of Lattice Systems

Course at Universität Heidelberg, Spring 2010

Instructor

Manfred Salmhofer

Contents

This course covers classical and quantum statistical mechanics for lattice systems, i.e. systems on a discrete position space, which arise naturally in solid state physics. In these models, many interesting phenomena and important concepts of statistical mechanics can be discussed in an elementary way, and important results can be shown without approximations. Topics include

  • the thermodynamic limit and phase transitions
  • DLR equations, mean-field theory, Peierls argument, expansion techniques
  • Zeroes of partition functions, Yang-Lee theory, Penrose-Lebowitz techniques.
  • Connections to large-deviation theory.
  • O(N)-models, quantum spin systems.
  • The Mermin-Wagner Theorem.
  • The infrared bound and continuous symmetry breaking

Prerequisites

Classical and quantum mechanics. Basics of Statistical Mechanics. The course will start with a brief recapitulation of the principles of equilibrium statistical mechanics.

Literature

D. Ruelle, Statistical Mechanics
B. Simon, The Statistical Mechanics of Lattice Gases
R.J. Baxter, Exactly Solved Models in Statistical Mechanics
O. Bratteli, D.W. Robinson, Operator Algebras and Quantum Statistical Mechanics I, II
Review and research articles in various journals (references will be given in class).

Coordinates

Time: Mondays 9:15-11:00, Thursdays 9:15-11:00
Place: Seminarraum des Instituts für theoretische Physik, Philosophenweg 19
Start: April 12, 2010