| SES # | TOPICS | LECTURE NOTES |
|---|---|---|
| L1 | Collective Behavior, from Particles to Fields Introduction, phonons and elasticity | (PDF) |
| L2 | Collective Behavior, from Particles to Fields (cont.) Phase transitions, critical behavior The Landau-Ginzburg Approach Introduction, saddle point approximation, and mean-field theory | (PDF) |
| L3 | The Landau-Ginzburg Approach (cont.) Spontaneous symmetry breaking and goldstone modes | (PDF) |
| L4 | The Landau-Ginzburg Approach (cont.) Scattering and fluctuations, correlation functions and susceptibilities, comparison to experiments | (PDF) |
| L5 | The Landau-Ginzburg Approach (cont.) Gaussian integrals, fluctuation corrections to the saddle point, the Ginzburg criterion | (PDF) |
| L6 | The Scaling Hypothesis The homogeneity assumption, divergence of the correlation length, critical correlation functions and self-similarity | (PDF) |
| L7 | The Scaling Hypothesis (cont.) The renormalization group (conceptual), the renormalization group (formal) | (PDF) |
| L8 | The Scaling Hypothesis (cont.) The Gaussian model (direct solution), the Gaussian model (renormalization group) | (PDF) |
| L9 | Perturbative Renormalization Group Expectation values in the Gaussian model, expectation values in perturbation theory, diagrammatic representation of perturbation theory, susceptibility | (PDF) |
| L10 | Perturbative Renormalization Group (cont.) Perturbative RG (first order) | (PDF) |
| L11 | Perturbative Renormalization Group (cont.) Perturbative RG (second order), the ε-expansion | (PDF) |
| L12 | Perturbative Renormalization Group (cont.) Irrelevance of other interactions, comments on the ε-expansion | (PDF) |
| L13 | Position Space Renormalization Group Lattice models, exact treatment in d=1 | (PDF) |
| L14 | Position Space Renormalization Group (cont.) The Niemeijer-van Leeuwen cumulant approximation, the Migdal-Kadanoff bond moving approximation | (PDF) |
| L15 | Series Expansions Low-temperature expansions, high-temperature expansions, exact solution of the one dimensional Ising model | (PDF) |
| L16 | Series Expansions (cont.) Self-duality in the two dimensional Ising model, dual of the three dimensional Ising model | (PDF) |
| L17 | Series Expansions (cont.) Summing over phantom loops | (PDF) |
| L18 | Series Expansions (cont.) Exact free energy of the square lattice Ising model | (PDF) |
| L19 | Series Expansions (cont.) Critical behavior of the two dimensional Ising model | (PDF) |
| L20 | Continuous Spins at Low Temperatures The non-linear σ-model | (PDF) |
| L21 | Continuous Spins at Low Temperatures (cont.) Topological defects in the XY model | (PDF) |
| L22 | Continuous Spins at Low Temperatures (cont.) Renormalization group for the coulomb gas | (PDF) |
| L23 | Continuous Spins at Low Temperatures (cont.) Two dimensional solids, two dimensional melting | (PDF) |
| L24 | Dissipative Dynamics Brownian motion of a particle | (PDF) |
| L25 | Continuous Spins at Low Temperatures (cont.) Equilibrium dynamics of a field, dynamics of a conserved field | (PDF) |
| L26 | Continuous Spins at Low Temperatures (cont.) Generic scale invariance in equilibrium systems, non-equilibrium dynamics of open systems, dynamics of a growing surface | (PDF) |