The Berezinskii-Kosterlitz-Thouless (BKT) Phase and its Domain of Attraction - Lecture 2

This lecture, the second in a four-part series by Christophe Garban from Université Lyon I, explores the mathematical approach to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in statistical physics. Delve into the fascinating world of spin systems on lattices and how they behave differently when spins belong to continuous spaces rather than discrete sets. Learn how the BKT phase transition, predicted in the 1970s, occurs in two-dimensional systems with Abelian continuous symmetry due to the behavior change of monodromies called "vortices." The complete series covers introduction to BKT transitions, mathematical approaches, domain of attraction, and non-linear sigma models, with examples including XY and Villain models, Coulomb gas, clock models, and integer-valued height functions. This 2-hour 9-minute scientific presentation from Institut des Hautes Etudes Scientifiques (IHES) provides valuable insights for researchers interested in statistical physics and phase transitions.