- Phase Transitions: General concepts of phase transitions, order parameter, continuous transition, Landau-Ginzburg (L-G) theory, concept of critical phenomena, critical exponents, Examples: mean field treatment of Ising model, etc.
., L-G theory for 1st order transition.
- Models: Exact solution of 1D Ising model by transfer matrix method, Discussion of 2D Ising, Potts model, etc.
- Partition function and etc: Partition function and L-G theory from the point of view of functional integral ( An example can be given in the context of Ising model)
- Symmetry breaking: Continuous symmetry breaking and sound mode, correlation function and correlation length, Example: Heisenberg system, O(N) model
- Fluctuations: Fluctuation phenomena: Gaussian fluctuations, Ginzburg criteria, upper and lower critical dimensions, Mermin-Wagner theorem.
- BKT transition in 2D, x-y model
- Liquids: pair correlation function, structure factor, etc.
- Linear response theory: Introduction, diffusion, fluctuation-dissipation
- Applications: Phase transition in liquid crystal, polymer physics, colloids, Superfluidity and L-G theory of superconductivity
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