PSI 2016/2017 - Statistical Mechanics (Kubiznak)

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

Basics of Statistical Physics: Gibbs Distribution, Statistical Ensembles

Thermodynamic Approach to Phase Transitions: Ideal Gas, Van der Waals fluid, Phase Transitions

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

Other Critical Exponents, Landau's Theory, Hubbard-Stratonovich Transformation

Spin-spin Correlation Function, Correlation Length, Landau-Ginsburg Functional

Wilsonian Renormalization 1: Goal, Integration over Fast Modes, Renormalized Couplings

Wilsonian Renormalization 2: Cummulant Expansion, Diagramatic Notation, RG Equations

Wilsonian Renormalization 3: Gaussian and Wilson-Fisher Fixed Points, Critical Exponents

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

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

Notion of Quantum Phase Transitions; Quantum Ising Model and Its Phase Diagram