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.

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  • 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

Statistical Field Theory on the Web

Some Classic Resources