SES # | TOPICS | KEY DATES |
---|---|---|
L1 | Collective Behavior, from Particles to Fields Introduction, phonons and elasticity | Problem set 1 out |
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 | Problem set 2 out |
L6 | The Scaling Hypothesis The homogeneity assumption, divergence of the correlation length, critical correlation functions and self-similarity | Problem set 1 due |
L7 | The Scaling Hypothesis (cont.) The renormalization group (conceptual), the renormalization group (formal) | |
L8 | The Scaling Hypothesis (cont.) The Gaussian model (direct solution), the Gaussian model (renormalization group) | |
R1 | Recitation | |
L9 | Perturbative Renormalization Group Expectation values in the Gaussian model, expectation values in perturbation theory, diagrammatic representation of perturbation theory, susceptibility | Problem set 2 due |
R2 | Recitation | |
E1 | In-class Test #1 | Problem set 3 out |
L10 | Perturbative Renormalization Group (cont.) Perturbative RG (first order) | |
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 | Problem set 4 out |
L13 | Position Space Renormalization Group Lattice models, exact treatment in d=1 | |
L14 | Position Space Renormalization Group (cont.) The Niemeijer-van Leeuwen cumulant approximation, the Migdal-Kadanoff bond moving approximation | Problem set 3 due |
R3 | Recitation | |
L15 | Series Expansions Low-temperature expansions, high-temperature expansions, exact solution of the one dimensional Ising model | |
L16 | Series Expansions (cont.) Self-duality in the two dimensional Ising model, dual of the three dimensional Ising model | Problem set 4 due |
R4 | Recitation | Problem set 5 out |
E2 | In-class Test #2 | |
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 5 due |
L20 | Continuous Spins at Low Temperatures The non-linear σ-model | Problem set 6 out |
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 | |
L23 | Continuous Spins at Low Temperatures (cont.) Two dimensional solids, two dimensional melting | |
L24 | Dissipative Dynamics Brownian motion of a particle | |
R6 | Recitation | |
L25 | Continuous Spins at Low Temperatures (cont.) Equilibrium dynamics of a field, dynamics of a conserved field | Problem set 6 due |
R6 | Recitation | |
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 |