Teaching

 Basic introduction to phase transitions: first order and continuous

 Phase transitions in equilibrium

•  Critical phenomena: critical exponents and scaling hypothesis

•  Ising model: exact solution in one dimension, discussion of the model in two dimensions

• Two-dimensional XY model and the Kosterlitz-Thouless transition

• Mean-field approximation and calculation of critical exponents

• Landau theory of phase transitions

• Renormalization group (preliminary ideas)

 Phase transitions out of equilibrium

•  Review of probability theory: Law of large numbers and the central limit theorem, Large deviations (introductory ideas)

• Stochastic processes: Markovian approximation, Master equation, Fokker-Planck equation, Langevin description, concept of steady states, detailed balance and equilibrium vs. nonequilibrium

•  Random walk, Brownian motion, Langevin and Fokker-Planck descriptions, Fluctuation-Dissipation theorem 

• Phase transitions in the asymmetric simple exclusion process and the zero-range process