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  • 3:52 PM, Sunday, 24 Oct 2021

Course Dual Degree (B. Tech + Master of Science / Master of Technology)
Semester Sem. VIII
Subject Code PH424
Subject Title Advanced Statistical Mechanics


Part 1: Phase Transitions and Critical Phenomena General Introduction:

Origin of phase transition, thermodynamic instabilites, Maxwell construction. Classification of phase transitions: first order and second order. Phase transitions in different systems (e.g. liquid-gas and paramagnet-ferromagnetic transition), order parameter, critical exponents, concept of long-range order.

Lattice models: Ising Model, exact solution in one dimension, high-temperature and low-temperature expansions. Phase transitions in X-Y and Heisenberg Models.

Mean field theory and Landau theory. Landau-Ginzburg theory for fluctutations.

Sponteneous symmetry breaking, Mermin-Wagner theorem.

Renormalization Group: scaling hypothesis and universality, renormalization group transformation. Upper and lower critical dimensions, epsilon-expansion, Ising model as example.

Quasi-long-range order, Kosterlitz-Thouless transition.

Part 2: Nonequilibrium Statistical Mechanics

Introduction to nonequilibrium, Markov Processes, Fokker Planck Equation, Langevin Equation, Master equation.

Linear response: Kubo formula, fluctuation-dissipation theorem.

Text Books

1. M. Plischke and B. Bergersen, Equilibrium Statistical Physics.

2. J. Cardy, Scaling and Renormalization in Statistical Physics.

3. R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics.

4. S-K Ma, Statistical Mechanics, World Scientific.


Same as References