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.

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 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

General Remarks


Homework Assignements

Lecture Notes

Send corrections and comments about this WEB page to Last updated 01/24/2020.