Advanced Topics in Statistical Mechanics

9 units (3-0-6) | second, third terms

The course covers rigorous results in classical and quantum statistical mechanics of lattice systems. Winter quarter: basic lattice models, existence of the thermodynamic limit, phase transitions at positive temperature, Hohenberg-Mermin-Wagner and Goldstone theorems. Spring quarter: C*-algebraic approach to statistical mechanics, locality and dynamics in quantum systems (Lieb-Robinson bounds), topological invariants of gapped quantum systems at zero temperature, Symmetry Protected Topological Phases. Not offered 2026-27.