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Explore advanced concepts in Statistical Mechanics through this graduate-level lecture from the 2025 Summer School at IMPA, 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. Drawing from renowned references like Feynman's Statistical Mechanics lectures, Presutti's work on scaling limits, and specialized texts on the Ising Model, master essential mathematical concepts that form the backbone of statistical mechanics. Part of a comprehensive master's program series, this 16th lecture session provides rigorous mathematical treatment of statistical mechanical principles, with additional requirements available for doctoral students.
