Lecture Notes

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)

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)