8.334: Statistical Physics II (Spring 2026)

Lecture 3

Symmetry Breaking

Phase diagrams of a simple ferromagnet

Coarse-grain to Landau-Ginzburg "Hamiltonian"

Saddle point integration (one variable) (SaddleInt1.pdf)

Mean-field approximation (MeanField1.pdf)

Critical exponents in mean-field (MFexponents.pdf)

Fluctuations and scattering line-shapes
- Notes on fluctuations
Continuous symmetry breaking and Goldstone modes

Breakdown of spontaneous symmetry breaking in low dimensions

Notes for lecture #3

8.334 - last update 2/5/26 by M. Kardar