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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, and specialized texts by Friedli and Velenik, master fundamental principles and advanced applications of statistical mechanics. Part of a comprehensive master's program at the Institute of Pure and Applied Mathematics (IMPA), this fourth lecture session provides rigorous mathematical foundations for understanding complex statistical mechanical systems.
