SS Mathematics )

**Requirements/prerequisites:** 441, some knowledge of metric spaces and norms

**Duration:** 21 weeks

**Number of lectures per week:** 3 hours per week, likely to be in one block and held at the
Dublin Institute for Advanced Studies, 10 Burlington Road

**Assessment:**

**End-of-year Examination:** End of year exam, 3 hours, may be held earlier than usual exams.

**Description: **

This is a new course (not the same topics as in 2002-3), and will be offered also to UCD students. That may place restrictions on the timing of the exam.

Course on Quantum Spin Systems

- Refresher of thermodynamics with emphasis on convexity.
- Hamiltonians for quantum lattice systems and existence of dynamics.
- Thermodynamic limit of the free energy.
- Entropy, the variational principle and tangent planes.
- The KMS condition and the relative Hamiltonian.
- Mean-field theory.
- Absence of phase transitions in 1 dimension.
- The Peierls argument.
- Reflection positivity.

Oct 6, 2004

File translated from T

On 6 Oct 2004, 17:50.