The calendar below provides information on the course’s lecture (L), recitation (R), and exam (E) sessions.
| SES # | TOPICS | KEY DATES |
|---|---|---|
| L1 |
Collective Behavior, from Particles to Fields
Introduction, Phonons and Elasticity |
|
| L2 |
Collective Behavior, from Particles to Fields (cont.)
Phase Transitions, Critical Behavior The Landau-Ginzburg Approach Introduction, Saddle Point Approximation, and Mean-field Theory |
|
| L3 |
The Landau-Ginzburg Approach (cont.)
Spontaneous Symmetry Breaking and Goldstone Modes |
|
| L4 |
The Landau-Ginzburg Approach (cont.)
Scattering and Fluctuations, Correlation Functions and Susceptibilities, Comparison to Experiments |
|
| L5 |
The Landau-Ginzburg Approach (cont.)
Gaussian Integrals, Fluctuation Corrections to the Saddle Point, The Ginzburg Criterion |
|
| R1 | Recitation | |
| L6 |
The Scaling Hypothesis
The Homogeneity Assumption, Divergence of the Correlation Length, Critical Correlation Functions and Self-similarity |
|
| L7 |
The Scaling Hypothesis (cont.)
The Renormalization Group (Conceptual), The Renormalization Group (Formal) |
Problem set 1 due |
| L8 |
The Scaling Hypothesis (cont.)
The Gaussian Model (Direct Solution), The Gaussian Model (Renormalization Group) |
|
| L9 |
Perturbative Renormalization Group
Expectation Values in the Gaussian Model, Expectation Values in Perturbation Theory, Diagrammatic Representation of Perturbation Theory, Susceptibility |
|
| R2 | Recitation | |
| L10 |
Perturbative Renormalization Group (cont.)
Perturbative RG (First Order) |
|
| R2 | Recitation | Problem set 2 due |
| R3 | Recitation (Review for Test) | |
| E1 | In-class Test 1 | |
| L11 |
Perturbative Renormalization Group (cont.)
Perturbative RG (Second Order), The ε-expansion |
|
| L12 |
Perturbative Renormalization Group (cont.)
Irrelevance of Other Interactions, Comments on the ε-expansion |
|
| L13 |
Position Space Renormalization Group
Lattice Models, Exact Treatment in d=1 |
|
| R4 | Recitation | |
| L14 |
Position Space Renormalization Group (cont.)
The Niemeijer-van Leeuwen Cumulant Approximation, The Migdal-Kadanoff Bond Moving Approximation |
|
| L15 |
Series Expansions
Low-temperature Expansions, High-temperature Expansions, Eexact Solution of the One Dimensional Ising Model |
Problem set 3 due |
| L16 |
Series Expansions (cont.)
Self-duality in the Two Dimensional Ising Model, Dual of the Three Dimensional Ising Model |
|
| L17 |
Series Expansions (cont.)
Summing over Phantom Loops |
|
| L18 |
Series Expansions (cont.)
Exact Free Energy of the Square Lattice Ising Model |
|
| R5 | Recitation | |
| L19 |
Series Expansions (cont.)
Critical Behavior of the Two Dimensional Ising Model |
Problem set 4 due |
| L20 |
Continuous Spins at Low Temperatures
The Non-linear σ-model |
|
| L21 |
Continuous Spins at Low Temperatures (cont.)
Topological Defects in the XY Model |
|
| L22 |
Continuous Spins at Low Temperatures (cont.)
Renormalization Group for the Coulomb Gas |
|
| R6 | Recitation (Review for Test) | |
| E2 | In-class Test 2 | |
| R7 | Recitation | |
| L23 |
Continuous Spins at Low Temperatures (cont.)
Two Dimensional Solids, Two Dimensional Melting |
Problem set 5 due |
| L24 |
Dissipative Dynamics
Brownian Motion of a Particle |
|
| R8 | Recitation | |
| L25 |
Continuous Spins at Low Temperatures (cont.)
Equilibrium Dynamics of a Field, Dynamics of a Conserved Field |
|
| R9 | Recitation | Problem set 6 due |
| E3 | In-class Test 3 | |
| L26 |
Continuous Spins at Low Temperatures (cont.)
Generic Scale Invariance in Equilibrium Systems, Non-equilibrium Dynamics of Open Systems, Dynamics of a Growing Surface |
Final project due 2 days after L26 |
