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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. Drawing from renowned references like Feynman's Statistical Mechanics lectures, Presutti's work on scaling limits, and specialized texts by Friedli and Velenik, master essential mathematical concepts that form the backbone of statistical mechanics. Part of a comprehensive master's program at IMPA (Instituto de Matemática Pura e Aplicada), this lecture offers rigorous mathematical treatment of statistical mechanical principles while maintaining the flexibility for additional requirements at the doctoral level.
