Calendar

Collective Behavior, from Particles to Fields (cont.)

Phase transitions, critical behavior

The Landau-Ginzburg Approach

Introduction, saddle point approximation, and mean-field theory

The Landau-Ginzburg Approach (cont.)

Scattering and fluctuations, correlation functions and susceptibilities, comparison to experiments

The Scaling Hypothesis

The homogeneity assumption, divergence of the correlation length, critical correlation functions and self-similarity

The Scaling Hypothesis (cont.)

The Gaussian model (direct solution), the Gaussian model (renormalization group)

Perturbative Renormalization Group

Expectation values in the Gaussian model, expectation values in perturbation theory, diagrammatic representation of perturbation theory, susceptibility

Perturbative Renormalization Group (cont.)

Perturbative RG (second order), the ε-expansion

Position Space Renormalization Group

Lattice models, exact treatment in d=1

Series Expansions (cont.)

Self-duality in the two dimensional Ising model, dual of the three dimensional Ising model

Series Expansions (cont.)

Exact free energy of the square lattice Ising model

Series Expansions (cont.)

Critical behavior of the two dimensional Ising model

Continuous Spins at Low Temperatures (cont.)

Topological defects in the XY model

Continuous Spins at Low Temperatures (cont.)

Two dimensional solids, two dimensional melting

Continuous Spins at Low Temperatures (cont.)

Generic scale invariance in equilibrium systems, non-equilibrium dynamics of open systems, dynamics of a growing surface