3 problems

Let $d\ge1$, let $\Omega^\star$ and $\Omega_{p,q}$ denote the sets of environments defined in the paper, and let $\mathrm{IIP}$ denote the invariance invariance principle establish…

Critical-point threshold conjecture. There is a $q_0=q_0(d)$ such that for $q>q_0$ there is non-uniqueness of Gibbs measures

Uniqueness conjecture. For $p\neq p_c$ there is a unique Gibbs measure.