Learning objectives for Statistical Physics 2
Chapter 3
- Explain what mean-field theory is
- The Ising Model Hamiltonian
- Derivation of expressions for magnetization in mean-field theory
- Explain what a critical exponent is
- Qualitatively understand the role of dimension in exact and mean-field theory
- Exact solution of 1D Ising model in zero field
- Derive how a general Landau theory gives rise to continuous and first-order phase transitions
- Read 3.9 qualitatively
- Definition of Landau-Ginzburg free energy
Chapter 4
- Understand how to get from (4.1) to (4.10)
- Physical basis of van der Waals equation
- Derivation of Maxwell construction
Chapter 5
- Definition of virial expansion
- Why and how is the expansion done in the Mayer function
- Qualitatively the diagram technique for dense gases
- Definition of the reduced distribution functions
- Qualitatively explain how the pair distribution function is linked to experimentally measurable quantities
Chapter 6
- Idea behind series expansions
- Idea behind high-temperature expansion
- Idea behind low-temperature expansion
- How to extract critical exponents from high-T expansion
- Derive the Rushbrooke inequality
- State the scaling hypothesis
- Understand how to derive (6.92)
- Explain what universality is
Chapter 7
- Explain idea behind the renormalization group
- Derive RG equation (7.13) for 1D Ising model
- Explain what an RG flow and a fixed point is
- Relation (7.32) between RG flow and critical exponents
Chapter 11
- (Skip all parts including second-quantized Hamiltonians)
- T_c for a noninteracting Bose gas
- Derive the Gross-Pitaevskii equation
- Connection between superfludity and excitation spectrum
- Familiar with some superfluid phenomena
- Landau-Ginzburg equations for a superconductor
- Understand how to derive the coherence length