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This lecture explores the domain of attraction of the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in statistical physics. Delve into the third part of a four-lecture series delivered by Christophe Garban from Université Lyon I at the Institut des Hautes Etudes Scientifiques (IHES). Learn how continuous-symmetry spin systems behave fundamentally differently from discrete models like the Ising model, particularly in two dimensions where the BKT transition occurs. Understand how this unique phase transition is caused by the behavior change of monodromies called "vortices." The complete series covers introduction to BKT transitions, mathematical approaches, domains of attraction, and non-linear sigma models with curvature. This two-hour lecture specifically focuses on the domain of attraction of the BKT phase, building on the foundational concepts established in the previous sessions about XY and Villain models, Coulomb gas, clock models, and integer-valued height functions.
