Stat Mech 2002

Course Contents

Part A. Basic Statistical Mechanics

Thermodynamics and phase transitions

Contents

Extensive and intensive quantities, equilibrium states and Gibbs spaces, stability conditions, the second law of thermodynamics, Legendre transforms. Phase transitions, order parameters, first and second order phase transitions. Scaling, homogeneous functions and critical indices.

References

  1. Thermodynamics, article by M.J. Buckingham in Phase Transitions and Critical Phenomena, Vol 2, eds. C. Domb and M.S. Green, Academic Press, 1972.
  2. Field Theory, the Renormalization Group and Critical Phenomena, by D. Amit, World Scientific, Singapore, 1984.
  3. B. Widom, Journal of Chemical Physics 43 (1965) 3898.
  4. Universal Critical-Point Amplitude Relations, article by V. Privman, P.C. Hohenberg and A.H. Aharony in Phase Transitions and Critical Phenomena, Vol 14, eds. C. Domb and J.L. Lebowitz, Academic Press, 1991.
  5. Scaling, Universality and Operator Algebras, article by L.P. Kadanoff, in Phase Transitions and Critical Phenomena, Vol 5A, eds. C. Domb and M.S. Green, Academic Press, 1975.

Basic probability

Contents

State space and counting, combining probabilities, conditional probabilities and independence, Bayes' theorem. Probability distribution functions, moments and cumulants, charactersitic function, generating functions. Central limit theorem, sampling and errors.

References

  1. Probability and its Engineering Uses by T.C. Fry, Van Nostrand, 1928.
  2. Probability and Statistics by M.H. DeGroot, Addison Wesley, 1986.
  3. Introduction to Probability Models by S.M. Ross, Academic Press, 1989.
  4. Random Processes by M. Rosenblatt, Oxford University Press, 1962.
  5. Probability and Measure by P. Billingsley, John Wiley and Sons, 1986.

Classical and quantum ensembles

Contents

Stationary ensembles; the microcanonical and canonical ensembles; computer simulations and the Metropolis algorithm; grand canonical ensembles.

References

  1. Statistical Mechanics by L. D. Landau and L. Lifschitz, Pergamon Press, 1977.
  2. Statistical Mechanics by R. K. Pathria, Pergamon Press, 1977.
  3. Statistical Mechanics by K. Huang, Wiley Eastern, 1988.
  4. Pauli Lectures on Physics: Vol 4. Statistical Mechanics by W. Pauli, ed. C.P. Enz, The MIT press, 1973.

Ideal gases

Contents

Statistical approach to thermodynamics of ideal gases, the partition function; Bose condesation and phase transitions; electrons in a magnetic field: Landau levels and applications.

References

  1. Statistical Mechanics by L. D. Landau and L. Lifschitz, Pergamon Press, 1977.
  2. Statistical Mechanics by R. K. Pathria, Pergamon Press, 1977.
  3. Statistical Mechanics by K. Huang, Wiley Eastern, 1988.
  4. Pauli Lectures on Physics: Vol 4. Statistical Mechanics by W. Pauli, ed. C.P. Enz, The MIT press, 1973.
  5. Quantum Theory of Solids by R. Peierls, Clarendon Press, 1955.

Part B. Critical phenomena and phase transitions

Introduction to lattice models

Contents

Random walks, scaling and critical exponents, continuum limit; percolation; spin models; gauge theories.

References

  1. Exactly solved models in statistical mechanics by R. J. Baxter
  2. Statistical field theory by C. Itzykson and J.-M. Drouffe
  3. Equilibrium statistical physics by M. Plischke and B. Bergersen

The Ising model

Contents

The Ising and Potts models, mean field theory, high and low temperature expansions, duality, Ginzburg-Landau theory, tricritical phenomena, the transfer matrix, Yang-Lee theory, real-space renormalisation.

References

  1. Exactly solved models in statistical mechanics by R. J. Baxter
  2. Statistical field theory by C. Itzykson and J.-M. Drouffe
  3. Equilibrium statistical physics by M. Plischke and B. Bergersen

O(N) models

Contents

O(N) models, Landau-Ginzburg theory, the renormalisation group, the Gaussian model and the Wilson-Fisher fixed point.

References

  1. Exactly solved models in statistical mechanics by R. J. Baxter
  2. Statistical field theory by C. Itzykson and J.-M. Drouffe
  3. Equilibrium statistical physics by M. Plischke and B. Bergersen
© Sourendu Gupta. Created on Jun 11, 2001.