Structure and Dynamics Group

Course requirements:

- Two problem sets
- One notebook

Notebook entries:

Weeks 1-3: 
- Describe the features of a (real space) renormalization map and its effect on observables.
- Describe a renormalization flow in parameter space.
- Outline the steps for obtaining critical exponents once the recursion relations describing the renormalization flow are obtained.

Weeks 4-5 (11-20 Sep):
- Outline the steps needed to obtain the scaling form for the free energy density of a 1D classical Ising model. 

Weeks 6-7 (25 Sep-4 Oct):
- Describe how the following techniques generate a suitable sample for estimating the thermodynamic properties of a system:
a) Molecular dynamics
b) Metropolis Monte Carlo

Problem Set 1 (due 25 Oct):
1) Consider a 2D classical Ising model with first- and second-nearest neighbor couplings, K1 and K2. Use renormalization transformations, ignoring higher-order generated terms, to obtain:
a) the recursion equations
b) all the fixed points
c) the linearized flow about the eigendirections of the fixed points
d) the scaling exponents yi
e) the non-zero critical temperature
2) Graph the renormalization flow of the previous model. Highlight the fixed points, eigenflow about the fixed points, and representative stream lines. 

Weeks 10-11 (30 Oct-8 Nov):
- Summarize the important physical properties of the:
(a) degenerate Fermi gas (jellium model) at high density
(b) ideal Fermi gas
(c) ideal Bose gas
(d) Gell-man and Low theorem 

Problem Set 2 (due 6 Dec):
1) Show that the retarded and advanced Green's functions satisfy Kramers-Kronig relations. Connect this proof with causality requirements.