| 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)
Perturbative Renormalization Group
Expectation Values in the Gaussian Model |
(PDF) |
| L9 |
Perturbative Renormalization Group (cont.)
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) |