Courses

Rigorous Results in Statistical Mechanics I: Equilibrium

Course ID/Name 

16:642:563

Description:

The course will cover traditional areas of statistical mechanics with a mathematical flavor. It will describe exact results where available and heuristic physical arguments where applicable. A rough outline is given below:

Course outline:

  1. Overview: microscopic vs. macroscopic descriptions; microscopic dynamics and thermodynamics.
  2. Energy surface; microcanonical ensemble; ideal gases; Boltzmann’s entropy, typicality.
  3. Alternate equilibrium ensembles; canonical, grand-canonical, pressure, etc. Partition functions and thermodynamics.
  4. Thermodynamic limit; existence; equivalence of ensembles; Gibbs measures.
  5. Cooperative phenomena: phase diagrams and phase transitions; probabilities, correlations and partition functions. Law of large numbers, fluctuations, large deviations.
  6. Ising model, exact solutions. Griffith’s, FKG and other inequalities; Peierle’s argument; Lee-Yang theorems.
  7. High temperature; low temperature expansions; Pirogov-Sinai theory.
  8. Fugacity and density expansions.
  9. Mean field theory and long range potentials.
  10. Approximate theories: integral equations, Percus-Yevick, hypernetted chain. Debye-Hückel theory.
  11. Critical phenomena: universality, renormalization group.
  12. Percolation and stochastic Loewner evolution.

If you have any questions about the course please email me: This email address is being protected from spambots. You need JavaScript enabled to view it.. We can then set up a time to meet.