This course deals with advanced topics in statistical mechanics. It is assumed that the student is familiar with graduate statistical mechanics, graduate quantum mechanics and one semester of quantum field theory. The first half of this lecture will be based on the book Phase Transitions and Renormalization Group by Nigel Goldenfeld. In the second half I will discuss more advanced topics. The first class will be on Monday January from 12.00 until 12.53 in P130.
| Phase Transitions | Langevin Equation |
| Critical Exponents | Metropolis Algorithm |
| Landau-Ginzberg Theory | Kadanoff Theory / Block Spins |
| 1d Ising Model | Renormalization Group Equations |
| 2d Ising Model | Renormalization Group Equation for the Ising Model |
| Kramers-Wannier Duality | Epsilon Expansion |
| Onsager Solution | Entanglement Entropy |
| XY Model | Ryu-Takayanagi Conjecture |
| Heisenberg Model | Statisical Mechanics of the SYK Model |
| Bethe Ansatz | Statistical Mechanics of Black Holes |
| Mermin-Wagner-Coleman Theorem | Spin Glasses |
| Kosterlitz-Thouless Transition | Lattice Models |
| Importance Sampling / Markov Chains | Conformal Symmetry |