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Title: Mathematical Statistical Mechanics by C. J. Thompson ISBN: 0-691-08219-7 Publisher: Princeton University Press Pub. Date: November, 1979 Format: Hardcover Volumes: 1 List Price(USD): $42.50

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Summary: Elementary introduction
Comment: This book gives an informal overview of the mathematical formalism of statistical mechanics with mathematical rigour not emphasized. There have been many developments in mathematical statistical mechanics since this book was published, particularly in the area of exactly solved models in statistical mechanics and vertex models. This book could be used as an introduction to these developments, in spite of the fact that the mathematics used in them is not covered in this book. Only very rudimentary mathematical tools are used therein. That is not to say that a beginning student interested in the mathematical aspects of statistical mechanics could not gain anything from the reading of the book. There are some very clear presentations of the following topics: 1. A detailed derivation of the Boltzmann equation. 2. A proof of the Poincare theorem, which states that a finite-energy mechanical system in a finite volume is recurrent. 3. A proof of the Liouville theorem, which gives the incompressibility of the flow of points in phase space. 4. A proof, using the Boltzmann "Stosszahlansatz", that the Kac ring model approaches equilibrium. 5. A proof of the existence of the thermodynamic limit for "van Hove potentials", i.e. those that have a hard core and an attractive tail. 6. The explicit calculation of the partition function for the Tonks and Takahashi gases, the Curie-Weiss model, and the one-dimensional Ising model. 7. The Onsager solution of the two-dimensional Ising model. 8. The combinatorial solution of the two-dimensional Ising model. 9. An Ising model for the DNA molecule.