6 problems

Lacoin's conjecture. At the critical point $\lambda=\lambda_w$, the interface should remain delocalized, but should be rigid about height

Let $\beta>\beta_c$. In the collapsed phase, the lower envelope is described by a wetting model with critical point $\widetilde\delta_c(\beta)$. Sharp-asymptotics conjecture. For e…

In the two-dimensional Blume–Capel model at the triple point $\lambda=\lambda_c$, the $+$ and $-$ phases may be separated by a mesoscopic layer of $0$ phase. For…

In the two-dimensional Ising metastability regime $B>B_0(\beta)$, with $\lambda(n)=B/n$, a macroscopic droplet is separated from the walls by a microscopic layer of the $-$ phase.…

For the two-dimensional Ising model with bulk field $\lambda\geq 0$, let $w(\lambda;\beta,h)$ denote the average thickness of the layer of unstable $-$ phase, and let…

In the three-dimensional Ising model, at sufficiently low temperature, a rigid interface separates the $+$ and $-$ bulk phases. In the partial wetting regime, the interface has a m…