Hi, I'm new to the forum, and I hope I'm not posting this under the wrong thread. I'm studying for quals, and I've come across this past exam: 1. The problem statement, all variables and given/known data http://www.physics.uiuc.edu/education/graduate/Qual/sm/SMSpring07B.pdf This is a problem on the Landau theory of phase transitions, and I have a good idea on how to do all the parts except part (b), though I have a feeling the solution to that is embarrassingly simple. 2. Relevant equations 3. The attempt at a solution Of course one way to attempt (b) is as a brute force counting problem; figure out the possible values of energy, and the number of configurations achieving those energies, and then sum to get the expectation value. But that's an insane way of doing it, since the number of configurations for achieving a certain energy is not so obvious (at least to me?). Thankfully the rest of the problem can be done without solving (b), but still I would like to know if anyone has any ideas. Thanks a lot!