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Lecture I : The Beresinskii-Kosterlitz-Thouless transition : the two-dimensional world and its peculiarities - Lara Benfatto - Jeudi 20 septembre 2018 à 10 h

INSP - Sorbonne Université - 4 place Jussieu - 75005 Paris - Barre 22-23, 3e étage, salle 317

Lara Benfatto
ISC-CNR and Sapienza University of Rome

More than 40 years after the seminal work by Berezinskii, Kosterlitz and Thouless the BKT transition remains one of the most spectacular phenomena in condensed matter systems, as it has been acknowledged by the 2016 Nobel Prize. Even though it was originally formulated within the context of the two dimensional XY model for classical spins, it represents the paradigm for the superfluid transition in two dimensions. As such, it has been the subject of an intense theoretical and experimental investigation in a variety of systems, ranging from thin films of superconductors to artificial heterostructures and cold atoms.

In the first lecture I will give an introduction to the basic mathematical ingredients needed to understand the occurrence of a BKT transition within the context of the classical 2D XY model. After discussing the difference between order and rigidity for a second-order phase transition, I will discuss the peculiar role of vortices in 2D and I will derive the mapping onto the Coulomb-gas model. Finally, I will sketch the main outcomes of the renormalization-group approach for the BKT phase transition.