Fluctuations and random processes. Brownian motion, - diffusion, random walks. Langevin equation, fluctuation dissipation
theorem, irreversibility. Markov processes, master equation. Fokker Planck equation. Examples of first order and continuous phase transitions. Mean field (van der Waals and Weiss molecular field) theories. Fluid magnet analogy. Correlations, classical (Ornstein Zemicke) theory. Statistical mechanical models :
Ising, lattice gas, Heisenberg, XY and Potts models. Transfer matrix
method, illustration using the onedimensional
Ising model. Duality in the twodimensional Ising model. High and low temperature series expansions. Critical phenomena: longrange
order, order parameter, scaling, universality, critical exponents. Peierls argument for phase transitions. Spontaneous breakdown of symmetry, Landau theory of phase transitions. Role of fluctuations, lower and upper critical dimensions. GinzburgLandau model. Higgs mechanism, examples. Merminwagner theorem. Topological (BerezinskiKosterlitzThouless)
phase transition. Elements of the renormalization group approach to
continuous phase transitions : flows in parameter space, fixed points,
epsilon expansion, realspace
renormalization. Connection with
Euclidean field theories. Elementary ideas on percolation.
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- Teacher: gupte Neelima M Gupte