# Lecture Notes

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)

#### Learning Resource Types

assignment Problem Sets