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Explore advanced concepts in Statistical Mechanics in this graduate-level lecture from IMPA's 2025 Summer School, delivered in Portuguese by Professor Hubert Lacoin. Delve into Hamiltonian systems, Liouville's theorem, Poincaré recurrence theorem, Birkhoff's theorem, Boltzmann hypothesis, statistical ensembles, Gibbs measure, Ising model, thermodynamic limit, FKG inequality, phase transitions, phase diagrams, FK models, and Pirogov-Sinai theory. Drawing from renowned references including Feynman's Statistical Mechanics lectures, Presutti's work on scaling limits, Friedli's elements of statistical mechanics, and Velenik's study of the Ising model, gain comprehensive insights into fundamental mathematical principles underlying statistical mechanics. Part of a master's degree program at the Institute of Pure and Applied Mathematics (IMPA), this lecture serves as the 22nd session in a series exploring the mathematical foundations of statistical mechanics.
