Introduction to Mathematical Statistical Physics (Paperback)

The subject and the main notions of equilibrium statistical physics: Typical systems of statistical physics (Phase space, dynamics, microcanonical measure) Statistical ensembles (Microcanonical and canonical ensembles, equivalence of ensembles) Statistical ensembles-Continuation (the system of indistinguishable particles and the grand canonical ensemble) The thermodynamic limit and the limit Gibbs distribution The existence and some ergodic properties of limiting Gibbs distributions for nonsingular values of parameters: The correlation functions and the correlation equations Existence of the limit correlation function (for large positive $\mu$ or small $eta$) Decrease of correlations for the limit Gibbs distribution and some corollaries (Representativity of mean values, distribution of fluctuations, ergodicity) Thermodynamic functions Phase transitions: Gibbs distributions with boundary configurations An example of nonuniqueness of Gibbs distributions Phase transitions in more complicated models The ensemble of contours (Pirogov-Sinai theory) Deviation: The ensemble of geometric configurations of contours The Pirogov-Sinai equations (Completion of the proof of the main theorem) Epilogue. What is next? Bibliography Index.