4 problems

Consider the low-temperature three-dimensional Ising model with Dobrushin boundary conditions inducing a horizontal interface between the $+$ and $-$ phases. Let the roughening tem…

Let $\Pi=\{x\in\mathbb{Z}^d:x_1\geq 0\}$ be a half-space, and let $\Lambda'_n\supset\{-n,\ldots,n\}^d$ satisfy … Fix boundary conditions $\tau$ equal to $0$ on $\Pi$ and $1$ on…

Crossing and displacement exponent conjecture. There exist $\nu,\delta>0$ such that

Let $B_L$ be the rhombic region of scale $L$, and let $Z_L$ denote the voter-model interface curve in $B_L$. Straight-line convergence conjecture. As $L\rightarrow\infty$, the inte…