Statistical Mechanics and Critical Phenomena

Basic course given by Giuseppe Santoro, Alessandro Silva

Term: 1

Start: 09-10-2017 End: 21-12-2017 Room: 131

Credits: 6

Schedule: Tue 14:00 - 16:00, Wed 14:30 - 16:30


Part 1

  • Review of Thermodynamics
  • Ensembles: microcanonical, canonical, and grandcanonical, and their equivalence
  • Applications to gases and magnets: ideal gases and the Ising model
  • Phase transitions, universality and critical phenomena
  • Transfer matrix method and quantum-classical correspondence
  • Mean Field Theory
  • Landau Ginzburg Theory of phase transitions: Ising model and phi^4-field theory
  • Quantum statistical mechanics: Bose-Einsetin and Fermi-Dirac statistics
  • Applications: Bose-Einstein condensation, Debye theory, etc

Part 2

  • Critical phenomena and renormalisation: generalities about the renormalisation group
  • Block spin transformations and real space renormalisation group.
  • Applications to the Ising model
  • Numerical techniques
  • Momentum space renormalisation and the epsilon expansion with applications to various models
  • The XY model and the Kosterlitz-Thouless transition

Part 3

  • The transverse field quantum Ising model: statics and dynamics.
  • Classical-quantum mapping and derivation of a Suzuki-Trotter path-integral
  • Jordan-Wigner transformation in 1d and mapping into a BCS fermionic problem
  • Topological aspects in 1d and Majorana fermions in the ferromagnetic phase
  • Monte Carlo approaches based on Swendsen-Wang cluster algorithm in higher dimensions, including the time-continuum limit algorithm of Rieger-Kawashima

Online resources

Filename Size Date Modified
LNotes_SM.pdf 5.24 MB 2018-02-05 15:53:45