Infrared bounds, reflection positivity and continuous symmetry breaking in classical and quantum spin systems

Lectures at the Prague Summer School on Mathematical Physics -- 1996

Prague, October 20-26, 1996

(Hand written lecture notes)



1. Classical Heisenberg models: the theorem of Fröhlich, Simon and Spencer.

2. Quantum Heisenberg models: intro; long range order parameter; quantum correlation inequalities (Bogoliubov, Falk-Bruch)

3. Quantum Heisenberg models continued: the theorem of Mermin and Wagner; the theorem of Dyson, Lieb and Simon (and its extensions)