3 problems

Fix $\delta>0$ and $c>0$, and consider the probability distribution $\mathbb Q_{\beta,\delta,c,N}^{+,n}$ on $n$ ordered level-line paths $\eta_1,\ldots,\eta_n$ with weights combini…

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…

Consider the two-dimensional Ising model in the complete wetting regime with $h\geq h_{\mathrm{w}}(\beta)$ and positive bulk field $\lambda$. Let $\gamma^+$ be the upper envelope o…