# Lecture Notes

SES # | TOPICS | LECTURE NOTES |
---|---|---|

L1 |
## Collective Behavior, from Particles to FieldsIntroduction, phonons and elasticity |
(PDF) |

L2 |
## Collective Behavior, from Particles to Fields (cont.)Phase transitions, critical behavior ## The Landau-Ginzburg ApproachIntroduction, 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 HypothesisThe 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) |
(PDF) |

L9 |
## Perturbative Renormalization GroupExpectation 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 GroupLattice 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 ExpansionsLow-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 TemperaturesThe 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 DynamicsBrownian motion of a particle |
(PDF) |

L25 |
## Continuous Spins at Low Temperatures (cont.)Equilibrium dynamics of a field, dynamics of a conserved field |
(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 |
(PDF) |