Palestra ministrada pelo Prof. Dr. Nicolás Wschebor da Universidad de la República, Uruguay.
Resumo: In this introductory talk I will present a review of the most important ideas in the statistical-mechanical analysis of phase transitions. Paradigmatic models on the topic will be presented (including the famous Ising model, having its 100 years in 2020) and the basic problems introduced. Most common transitions (appearing in very different realms of physics) will be presented pointing out their formal similarities. Notions as spontaneously broken symmetries, second order phase transitions (or critical phenomena) and universality will be introduced. Finally, a survey of the most recent theoretical results in the topic will be sketched (including high order perturbative calculations, Conformal Boostrap methods and Wilsonian Functional Renormalization Group approaches).