The lecture notes are from an earlier version of this course, but still correspond to the topics covered in this version.
| SES # | TOPICS | LECTURE NOTES |
|---|---|---|
| L1 |
Collective Behavior, from Particles to Fields
Introduction, Phonons and Elasticity |
Lecture Note 1 (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 |
Lecture Note 2 (PDF) |
| L3 |
The Landau-Ginzburg Approach (cont.)
Spontaneous Symmetry Breaking and Goldstone Modes |
Lecture Note 3 (PDF) |
| L4 |
The Landau-Ginzburg Approach (cont.)
Scattering and Fluctuations, Correlation Functions and Susceptibilities, Comparison to Experiments |
Lecture Note 4 (PDF) |
| L5 |
The Landau-Ginzburg Approach (cont.)
Gaussian Integrals, Fluctuation Corrections to the Saddle Point, The Ginzburg Criterion |
Lecture Note 5 (PDF) |
| L6 |
The Scaling Hypothesis
The Homogeneity Assumption, Divergence of the Correlation Length, Critical Correlation Functions and Self-similarity |
Lecture Note 6 (PDF) |
| L7 |
The Scaling Hypothesis (cont.)
The Renormalization Group (Conceptual), The Renormalization Group (Formal) |
Lecture Note 7 (PDF) |
| L8 |
The Scaling Hypothesis (cont.)
The Gaussian Model (Direct Solution), The Gaussian Model (Renormalization Group) |
Lecture Note 8 (PDF) |
| L9 |
Perturbative Renormalization Group
Expectation Values in the Gaussian Model, Expectation Values in Perturbation Theory, Diagrammatic Representation of Perturbation Theory, Susceptibility |
Lecture Note 9 (PDF) |
| L10 |
Perturbative Renormalization Group (cont.)
Perturbative RG (First Order) |
Lecture Note 10 (PDF) |
| L11 |
Perturbative Renormalization Group (cont.)
Perturbative RG (Second Order), The ε-expansion |
Lecture Note 11 (PDF) |
| L12 |
Perturbative Renormalization Group (cont.)
Irrelevance of Other Interactions, Comments on the ε-expansion |
Lecture Note 12 (PDF) |
| L13 |
Position Space Renormalization Group
Lattice Models, Exact Treatment in d=1 |
Lecture Note 13 (PDF) |
| L14 |
Position Space Renormalization Group (cont.)
The Niemeijer-van Leeuwen Cumulant Approximation, The Migdal-Kadanoff Bond Moving Approximation |
Lecture Note 14 (PDF) |
| L15 |
Series Expansions
Low-temperature Expansions, High-temperature Expansions, Exact Solution of the One Dimensional Ising Model |
Lecture Note 15 (PDF) |
| L16 |
Series Expansions (cont.)
Self-duality in the Two Dimensional Ising Model, Dual of the Three Dimensional Ising Model |
Lecture Note 16 (PDF) |
| L17 |
Series Expansions (cont.)
Summing Over Phantom Loops |
Lecture Note 17 (PDF) |
| L18 |
Series Expansions (cont.)
Exact Free Energy of the Square Lattice Ising Model |
Lecture Note 18 (PDF) |
| L19 |
Series Expansions (cont.)
Critical Behavior of the Two Dimensional Ising Model |
Lecture Note 19 (PDF) |
| L20 |
Continuous Spins at Low Temperatures
The Non-linear σ-model |
Lecture Note 20 (PDF) |
| L21 |
Continuous Spins at Low Temperatures (cont.)
Topological Defects in the XY Model |
Lecture Note 21 (PDF) |
| L22 |
Continuous Spins at Low Temperatures (cont.)
Renormalization Group for the Coulomb Gas |
Lecture Note 22 (PDF) |
| L23 |
Continuous Spins at Low Temperatures (cont.)
Two Dimensional Solids, Two Dimensional Melting |
Lecture Note 23 (PDF) |
| L24 |
Dissipative Dynamics
Brownian Motion of a Particle |
Lecture Note 24 (PDF) |
| L25 |
Continuous Spins at Low Temperatures (cont.)
Equilibrium Dynamics of a Field, Dynamics of a Conserved Field |
Lecture Note 25 (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 |
Lecture Note 26 (PDF) |
