Renormalization Group Methods in Statistical Field Theory

Fall 2006 lectures at the Feza Gürsey Institute by Michael Hinczewski

General information


Problem sets

Problem set solutions

Quiz solutions




Michael Hinczewski homepage

Feza Gürsey Institute


  • historical motivation: phase transitions, critical exponents, universality

  • order parameters and effective field theories, Landau-Ginzburg Hamiltonian, mean-field approximation, fluctuations and the breakdown of mean-field theory

  • scaling hypothesis and critical exponent relations

  • Kadanoff scaling theory, position-space renormalization group techniques, Migdal-Kadanoff procedure

  • φ4 scalar field theory, Wilson momentum-space renormalization, epsilon expansion

  • fermionic field theory: Grassmann numbers, fermion coherent states and path integrals

  • renormalization group for one-dimensional interacting fermions, the Luttinger liquid

  • interacting fermions in higher dimensions, Landau Fermi-liquid theory and the superconducting instability from a renormalization group approach

Course references

P.M. Chaikin and T.C. Lubensky, "Principles of condensed matter physics", Cambridge University Press (1995).

R. Shankar, "Renormalization group approach to interacting fermions", Rev. Mod. Phys. 66, 129 (1994).