Phase transition and critical behavior in hierarchical integer-valued Gaussian and Coulomb gas models

Marek Biskup, Haiyu Huang

Given a square box $\hat{I}{›}_n\subseteq {\mathbb{Z}}^2$ of side length $L^n$ with $L,n>1$, we study hierarchical random fields $\{\ddot{I}{•}_x:x\in \hat{I}{›}_n\}$ with law proportional to ${\rm e}^{\f…