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) |