4 problems

Smooth-phase conjecture. Every ergodic gradient Gibbs measure is in a smooth phase in every dimension $d\geq 3$; equivalently, each such measure is the restriction of a non-gradien…

Frozen-region conjecture. The model exhibits a phenomenon similar to the frozen region in the original dimer model.

Conjectural two-dimensional fluctuation theorem. The centered random height function, multiplied by $\sqrt{\pi}$, converges in distribution to the pullback under $\Omega$ of the Ga…

Benjamini–Yadin–Yehudayoff conjecture. On any graph $G$, the typical ranges of the random homomorphism and Lipschitz height functions are of the same order of magnitude.