Subject Code: PH7L004 Subject Name: Advanced Statistical Physics L-T-P: 3-0-0 Credit: 3
Pre-requisite(s): Nil
Phase transitions in various dimensions: Magnetic systems and liquid-gas transitions. Correlation Functions.  Landau theory of phase transitions. Calculation of critical exponents; Examples: Examples of first order and continuous phase transitions. Mean field (van der Waals and Weiss molecular field) theories. Fluid- magnet analogy. Correlations. Classical (Ornstein-Zernicke) theory; Statistical mechanical models: Ising, lattice gas, Heisenberg, XY and Potts models. Transfer matrix method. illustration using the one-dimensional lsing model. Duality in the two-dimensional Ising model. High and low temperature series expansions; Critical phenomena: long-range 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. Ginzburg-Landau model. Higgs mechanism, examples. Mermin-wagner theorem. Topological (Berezinski-Kosterlitz-Thouless) phase transition; Introduction to Renormalization Group: Fixed points. Relevant and Irrelevant variables. Relation between Critical exponents from RG.  Momentum space RG: Going from discrete to continuous picture. Partition function. Functional integration. Landau-Ginzburg model. Consistency with Landau model. Scaling in momentum space. Dimensional analysis. Scaling and Anomalous dimensions. Evaluation of Partition Function in the Gaussian model. RG treatment of the Gaussian model.
Text Books/Reference Books:
  1. Goldenfeld Nigel, Lectures on Phase Transition and Renormalization Group, Westview Press.
  2. Mehran Kardar, Statistical Physics of Fields, Cambridge University Press.
  3. Pathria R. K. & Beale P. D., Statistical Mechanics, Academic Press.
  4. Stanley H. E., Introduction to Phase Transitions and Critical Phenomena, Clarendon Press, Oxford.
  5. Chaikin P. M. & Lubensky T. C., Principles of Condensed Matter Physics, Cambridge University Press.
  6. McComb W. D., Renormalization Methods: A Guide for Beginners, Oxford University Press, USA.