David Tong: Lectures on Statistical Field Theory

These lecture notes provide a detailed introduction to phase transitions and the renormalisation group, aimed at "Part III" (i.e. masters level) students. The lecture notes come in around 130 pages and can be downloaded below.

PDF       HTML

Content

• 1. From Spins to Fields:   PDF
  Introduction; The Ising Model; Landau Mean Field Theory, Universality, Critical Exponents; Landau-Ginzburg Theory, Domain Walls, The Lower Critical Dimension.
• 2. My First Path Integral:   PDF
  The Thermodynamic Free Energy (again); Correlation Functions, Correlation Length; The Upper Critical Dimension; The Analogy with Quantum Field Theory.
• 3. The Renormalisation Group:   PDF
  The Big Idea, Universality Explained, Scaling Explained; Relevant, Irrelevant and Marginal; The Gaussian Fixed Point, Dangerously Irrelevant Operators; Interactions, Feynman Diagrams; the Epsilon Expansion, the Wilson-Fisher Fixed Point, d=2; A Sniff of Conformal Symmetry.
• 4. Continuous Symmetry:   PDF
  The Importance of Symmetry; O(N) Models, Goldstone Bosons and Goldstone's Theorem, The Mermin-Wagner Theorem; Sigma Models, Background Fields, Large N; the Kosterlitz-Thouless Transition, Vortices, the Coulomb Gas, the Sine-Gordon Model, RG for KT and SG.

Problem Sheets

• Problem Sheet 1:   Postscript    PDF    Mean Field Theory


• Problem Sheet 2:   Postscript    PDF    Mostly Scaling


• Problem Sheet 3:   Postscript    PDF    RG

Statistical Field Theory on the Web

• Statistical Field Theory  a previous Cambridge course by Ron Horgan


• Statistical Field Theory  by Mehran Kardar at MIT


• Phase Transitions and Collective Phenomena   by Ben Simons at Cambridge


• The Renormalization Group John McGreevy at San Diego


• Advanced Statistical Mechanics   by Martin Grant at McGill


• 6 Lectures on QFT, RG and SUSY   by Tim Hollowood


• Introduction to Renormalization    by Simon DeDeo, giving an insight into the many broad applications of RG.


• Simulation of the Potts Model   by Alexander Farren, Mikey Whelan, Luke Hodgkiss

Some Classic Resources

• Nobel Prize Lecture   by Ken Wilson