David Tong: Statistical Field Theory

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.


PostScript      PDF

Content


  • 1. From Spins to Fields:   Postscript    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:   Postscript    PDF
    The Thermodynamic Free Energy (again); Correlation Functions, Correlation Length; The Upper Critical Dimension; The Analogy with Quantum Field Theory.
  • 3. The Renormalisation Group:   Postscript    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:   Postscript    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.


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