Contents: introduction and overview; Boltzmann factor, Boltzmann equation, and H theorem; Collisional equilibria. Liouville's theorem for Hamiltonian systems; BBGKY hierarchy of evolution equations for n-particle distribution functions; Hydrodynamics; Generalized dynamics: detailed balance; Brownian motion and Langevin equation; Example of linear response. Intro to phase transitions; More on mean-field theory; Correlation functions. Intro to rescaling; Landau theory. Ginzburg criterion. Critical exponents. Scaling hypothesis; Scaling hypothesis and rescaling transformations; Examples of dynamical critical exponents; Blume-Capel model: using RG to guess phase diagrams. 2D Ising self-duality; Continuous order parameters, e.g superconductivity and superfluidity; Gaussian model; RG for Gaussian model and beyond; Intro to polymers. Flory theory; More polymers: connecting SAWs to lattice magnets; Topological defects. |