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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 fundamental topics including 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. Draw from key 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. Part of a comprehensive master's program series, this eleventh lecture provides essential mathematical foundations for understanding statistical mechanical systems and their behavior.
