**PHY ****434: ****Advanced Statistical Mechanics**** (4)**

**Prerequisites (Desirable): **PHY 306 : Statistical Mechanics

*Learning Objectives*:

This course is about theoretical understanding of the various phases of matter using statistical mechanics. Phase transitions of the first order and second order will be discussed using phenomenological model and renormalization group approach. This course will also introduce non-equilibrium statistical mechanics.

*Course Contents*:

Revision of statistical mechanics, Thermodynamics of various ensembles, General properties of partition function, Lee-Young theorem.

Thermodynamics of phase transitions, metastable states, First and second order transitions, phenomenology of liquid-gas and paramagnetic-ferromagnetic transition, Van der Waals' equation of state critical point exponent.

Classical mean field theories, mean field theory for Ising model, Landau theory. Setting up the transfer matrix, Calculation of free energy and correlation functions, Results of Ising model in one and two dimensions.

Critical phenomena at second-order phase transitions, spatial and temporal fluctuations, scaling hypothesis, critical exponents, and universality classes. Ginzburg-Landau free-energy functional, momentum-space renormalization group.

Systems out of equilibrium, kinetic theory of a gas, approach to equilibrium and the H-theorem, Boltzmann equation and its application to transport problems. Brownian motion, Langevin equation, fluctuation-dissipation theorem, Einstein relation, Fokker-Planck equation.

*Suggested Books*:

- K. Huang, Statistical Mechanics.
- R.K. Pathria, Statistical Mechanics.
- E.M. Lifshitz and L.P. Pitaevskii, Physical Kinetics.
- D.A. McQuarrie, Statistical Mechanics.
- L.P. Kadanoff, Statistical Physics: Statistics, Dynamics and Renormalization.
- P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics.
- H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena

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