Introdução à Mecânica Estatística - Aula 14

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. Master's level content includes core statistical mechanical principles while doctoral studies incorporate additional advanced requirements.