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Institut für Mathematik

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Mathematical Physics II: Mathematical Statistical Mechanics   (SS 2012)


Lectures   Dr. Matteo Petrera Mon  12:15 - 13:45  MA 645
  Dr. Matteo Petrera Wed  12:15 - 13:45  MA 744
Tutorial    ------------------------   ---   -----------------  -----------

This is a course of the Berlin Mathematical School held in English.

Office hours

Name Office hours Room
Lectures   Dr. Matteo Petrera                     Thu 10:00 - 12:00   MA 819
Tutorial    -----------------------    -------------------------------------------------    ---------


  • Measure spaces, Probability spaces, Measurable dynamical systems, Ergodic systems, Entropy.

  • Maxwell-Boltzmann kinetic theory, Boltzmann transport equation, Boltzmann gas, Boltzmann H Theorem, Kac ring.

  • Gibbs ensembles, Ergodic hypothesis, Microcanonical ensemble, Canonical Ensemble, Grand canonical ensemble, Thermodynamic limit, Phase transitions.

  • Ising-type models, Gibbs ensembles for Ising models, One-dimensional Ising model, Dimer statistics, Two-dimensional Ising model.


You are invited to consult the following references and books. If you have problems in getting them please do not hesitate to contact me.
  • M. Petrera, Lecture Notes (complete version, pwd protected file).
  • G. Gallavotti, Statistical Mechanics: a Short Treatise, Springer, 1999.
  • D. Ruelle, Statistical Mechanics: Rigorous Results, Benjamin, 1969.
  • C.J. Thompson, Mathematical Statistical Mechanics, MacMillan, 1972.
  • R. Kubo, Statistical Mechanics, Elsevier, 1965.
  • B. McCoy, Advanced Statistical Mechanics, Oxford, 2010.
  • M. Baus, C.Tejero, Equilibrium Statistical Physics, Springer, 2008.


Homework sheets

Homework policy

  • There is no Tutorial. Written homework sheets will be assigned every two weeks.
  • Homeworks may be turned in directly to the lecturer.
  • To get the Übungsschein, you need to satisfactorily complete 50% of the homework assignments.

Matteo Petrera . 06.07.2012