Surface Law and Charge Rigidity for the Coulomb Gas on Zd

I will start by introducing and motivating the (two-component) Coulomb gas on the d-dimensional lattice Zd. I will then present some puzzling properties of the fluctuations of this Coulomb gas. The connection of this model with integer-valued fields and compact-valued spin systems will be emphasised through the talk. This is based on joint works with Avelio Sepúlveda and David Dereudre