PHZ3400: Midterm Review
Folks,
I noticed that both the lecture notes and the homework solutions related to ferromagnetism and the Ising model remain incomplete. The upcoming make-up midterm exam will have questions on the following:
- spontaneous symmetry breaking - electrons must pick a spin
- thermodynamic limit - phase transition to a ferromagnetic state is only possible thru infinite number of spins
- domain wall argument for the relaxation time below Tc - domain wall is useful to make all spins switch direction, must overcome free energy barrier. Time diverges exponentially to L, system size, which is proportional to wall.
- Curie temperature - Within mean-field theory, the Curie temperature of a ferromagnet is proportional the magnetic exchange interaction and the coordination number (number of neighbors at any given site) of the lattice in question.
- effects of an external symmetry-breaking field - 2nd order phase transition only found when h = 0
In addition, you need to know the following:
- Concept of Fermi-Dirac and Bose-Einstein statistics
- the corresponding F-D and B-E distribution functions
- how this affects finite temperature properties
- The significance of the Fermi energy is most clearly seem by setting T=0. At absolute zero, the probability is =1 for energies less than the Fermi energy and zero for energies greater than the Fermi energy. We picture all the levels up to the Fermi energy as filled, but no particle has a greater energy. This is entirely consistent with the Pauli exclusion principle where each quantum state can have one but only one particle.
- The Bose-Einstein distribution describes the statistical behavior of integer spin particles (bosons). At low temperatures, bosons can behave very differently than fermions because an unlimited number of them can collect into the same energy state, a phenomenon called "condensation".
- Pauli Exclusion Principle
Also, both for vibrations and quantum electrons:
- quantization of wave-vectors
- how to go from a sum over k to an integral in the limit L->infinity
- how to calculate the Debye temperature and the Fermi temperature
Again, all derivations given in class must be familiar, and the test will very effectively determine if you know the material or not. If any of the above is not familiar, is confusing, and you cannot reproduce the derivations presented in class (without looking at the notes!), then you are not well prepared for this test.
On the original mid-term exam it became very clear that the majority of people were not sufficiently familiar with the material/derivations presented in class. If this does not change, then the make-up exam will have a similar outcome. I also want to make it abundantly clear to you all that those who have less then 50% on the tests will not pass this class!
So hit the books and make a serious effort to catch up on what you missed on the original mid-term. if you do better on the make up midterm, I will simply scratch (eliminate) your grade from the original midterm and replaced it with the improved one.
Good luck!
Vlad