Free energy analyticity of the disordered XY and 2D Coulomb gas models.

par Lucas D'Alimonte (ICJ)

mardi 29 sept. 2026, 09:50 → 10:50 Europe/Paris

Amphi Schwartz

In this talk, I will consider three models of statistical mechanics: the classical XY model in arbitrary dimension, the lattice Coulomb gas in dimension two, and the square well model in arbitrary dimension. For each of these three models, we prove that the free energy is analytic in the disordered regime (the square well model is disordered at any positive temperature). In order to prove these results, we prove that the Gibbs measures of these models are factors of i.i.d. with information clusters of exponentially decaying volume. In the case of the Coulomb gas, this also implies that the charge interactions decay exponentially fast in the distance when the temperature is strictly above the Berezinskii–Kosterlitz–Thouless transition temperature.

I will give a gentle introduction to those three models, and explain the proof in the simpler setting of the square-well model. Based on a joint work with Piet Lammers.