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Explore the fascinating Berezinskii-Kosterlitz-Thouless (BKT) phase transition in this 59-minute lecture presented by Christophe Garban at the Hausdorff Center for Mathematics. Delve into the world of statistical physics to understand how spins along the lattice ℤ^d interact and fluctuate with temperature changes. Learn how continuous symmetry spin systems (like the XY model with unit circle S^1 spins or the classical Heisenberg model with unit sphere S^2 spins) exhibit drastically different phase transition behaviors compared to discrete symmetry systems like the Ising model. Discover the groundbreaking BKT phase transition predicted in the 1970s for two-dimensional systems, which occurs due to behavioral changes in monodromies called "vortices." This first part of the lecture introduces the BKT phase transition, explains key ideas behind recent existence proofs, and discusses the latest findings in this intriguing area of mathematical physics.
