Kosterlitz-Thouless transition and statistical reconstruction of the Gaussian free field

Abstract: The Berezinskii-Kosterlitz-Thouless transition (BKT transition) is a phase transition which occurs in dimension two for spin systems such as the plane rotator model (or XY model). This phase transition was discovered by these three physicists as the first example of a topological phase transition and was rigorously understood by Fröhlich and Spencer in the 80's. I will spend the main part of my talk explaining what are these topological phase transitions. I will then survey the contributions of Fröhlich and Spencer to this theory and I will end with new results we obtained recently with Avelio Sepúlveda in this direction. The talk will be based mostly on the preprint: arxiv.org/abs/2002.12284

dynamical systemsprobability

Audience: researchers in the topic

( paper | slides | video )

Horowitz seminar on probability, ergodic theory and dynamical systems