In the first half of the talk we will introduce the Berezinskii-Kosterlitz-Thouless phase transition as our motivation. We will then revisit the classical phenomenon of duality between random integer-valued height functions with positive definite potentials and abelian spin models with O(2) symmetry.
In the second half, we will apply this to derive new results in quite high generality.
In particular, we will discuss how to obtain GFF upper bounds on the variance of the height function, and then use it to give a new proof of the BKT transition.
In the latter we use as input the recent delocalisation result of Piet Lammers.
The talk is based on https://arxiv.org/abs/2303.08596.