The Berezinskii-Kosterlitz-Thouless (BKT) Phase and its Domain of Attraction - Lecture 4

This lecture, the fourth in a series by Christophe Garban from Université Lyon I, explores non-linear sigma models and curvature in relation to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. Delve into the mathematical framework of continuous symmetry spin systems, which behave fundamentally differently from discrete symmetry models like the Ising model. Learn how the BKT phase transition in two-dimensional systems is characterized by the behavior of vortices, particularly in Abelian symmetry cases. The lecture builds upon previous sessions that introduced the BKT transition, its mathematical approach, and its domain of attraction, completing a comprehensive examination of this intriguing phenomenon in statistical physics. This two-hour presentation is part of a scientific series available on CARMIN.tv, a French video platform specializing in mathematics and interdisciplinary research.