PHYS 217: Renormalization Group

Lecture Notes

• Introduction and RG perspective on random walks
• Self-avoiding random walks and their real-space RG
• Converting RG flows to phase diagrams
• Random walk as O(N) model
• Real space RG for 1d Ising model
• Real space RG for 2d Ising model
• Scaling of free energy
• Scaling of correlation functions
• Continuum limit of Ising model
• Critical exponents within Gaussian approx
• Breakdown of mean field theory
• Dangerously irrelevant operators and Gaussian model in d > 4
• Correction to scaling from irrelevant variables
• Crossover phenomena
• Finite size scaling
• Wilson RG for scalar phi4 theory
• Self-avoiding walk and phi4 theory
• Exponent eta in Wilson RG
• Continuous symmetry: general considerations
• Continuous sym: RG in 2 plus epsilon dim
• Introduction to O(2) model in d=2
• O(2) model in d = 2: duality and RG
• Operator product expansion
• A simple quantum phase transition
• Quantum phase transitions for bosons
• Phase transitions for bosons (continued) and Fermi liquid (brief)
• Introductory RG for disordered systems
• Disordered systems (continued)