Important Things to Note:
You can solve simple ising model problems using the canonical ensemble. It’s important to look at the derivation of the ising model and understand the statements about it being a “mean-field theory.” Harder ising model problems can be solved by using this thing called a “transfer matrix.” You’ll need to learn this too.
Review:
The ising model uses the canonical ensemble. So it’s not a bad idea to refresh yourself on how the canonical ensemble works. Make sure to reread the last part of the notes.
New Things to Learn:
Mean-field theory: Read Chapter 3 in Equilibrium Statistical Physics by Bergesen (sections 3.1-3.6). It’s a pretty mediocre book, but I haven’t really found much better for this topic.
Transfer Matrix: Read these excellent lecture notes from Hiram College.
Most important Problems & Solutions:
Basic Ising Model Problems (Just do Canonical Ensemble):
Transfer matrix Ising model:
- Do previous problems using the transfer matrix and compare your answer (it should be the same).
- Problem #2 (you can skip the stuff about density matrices for now)
Harder Ising Model Problems:
- Problem #3 in 2015 Fall Comprehensive Exam
- Problem 3.14 (the Potts Chain) of the “Equilibrium Statistical Physics” (I found this to be very helpful in understanding the transfer matrix) I’ll upload my scanned solutions soon.
