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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 treatment of the Ising model. Master essential mathematical concepts required for understanding complex statistical mechanical systems through this comprehensive graduate course lecture, which serves as part of IMPA's master's program curriculum.
