This course deals with advanced topics in statistical mechanics. It is assumed that the student is familiar with thermodynamics and equilibrium statistical mechanics as taught in the graduate course Statistical Mechanics (Phy540). 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 August 30 from 11.45 until 12.40 in P123.
The following is a list of topics I plan to discuss in the lecture:
| 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 | Stochastic Loewner Equation |
| XY Model | Growth Processes in 2d |
| Heisenberg Model | Random Partitions and Crystal Melting |
| Bethe Ansatz | Random Matrix Theory |
| Mermin-Wagner Theorem | Integrable Hierarchies |
| Kosterlitz-Thouless Transition | Non-Hermitian Random Matrix Theory |
| Importance Sampling / Markov Chains | Conformal Symmetry |
TA: to be announced
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With regards to holidays we will follow the offical University Calendar