PSI 2017/2018 - Statistical Mechanics (Kubiznak)

Review of Thermodynamics: Thermodynamic Laws, Temperature, Energy, Heat, Entropy

Basics of Statistical Physics: Liouville's Equation, Gibbs Distribution, Canonical Ensemble

Thermodynamic Approach to Phase Transitions: Ideal Gas, Van der Waals Fluid, Reentrant PT

Ising Model, Order Parameter, Mean Field Theory, Critical Exponent Beta

Critical Exponents, Landau's theory, Hubbard-Stratonovich Transformation

Spin-Spin Correlation Function, Correlation Length, Continuous Limit, Landau-Ginsburg Functional

Wilsonian Renormalization 1: Basic idea: Integration over Fast Modes, Flowing Couplings

Wilsonian Renormalization 2: Explicit calculation: Cumulant expansion, RG equations

Wilsonian Renormalization 3: Triumph: Wilson-Fisher Fixed Point, Critical Exponents

Vector Model, Goldstone Modes, CMW Theorem and Lower Critical Dimension

Near d=2, Vortices, Kosterlitz-Thoules Phase Transition

Bonus Lecture: Black Hole Thermodynamics