PHZ3400 Midterm Solution

PHZ 3400 – Phenomena in Condensed Matter

Midterm Exam – March 20, 2009

1. Give some examples of spontaneous symmetry breaking. How large must the system be to display spontaneous symmetry breaking?

2. Describe the difference between a first order and a second order phase transition. Give examples of each type.

3. What determines the Curie temperature of a ferromagnet? How does it depend on the coordination number of the corresponding crystal lattice?

4. What is the physical principle behind the fact that atoms act as hard spheres, i.e. they have a “core” impenetrable to other atoms?

5. Consider a one dimensional metal with electronic density n.

a. Determine the relation between the Fermi energy and the density in this case.

b. Determine the ground state kinetic energy as a function of density.

6. Consider a one dimensional vibrational system consisting with atoms of mass m connected by harmonic springs with spring constant K.

a. Determine the highest possible vibrational frequency of this system.

b. Sketch the motion of atoms corresponding to that mode.

c. Determine the low frequency speed of sound.

d. Determine the Debye temperature for this system.

e. Compute the temperature dependence of the specific heat at low temperatures.

f. Compute the temperature dependence of the specific heat at high temperatures.