7 problems

For a zero-temperature square-lattice Potts antiferromagnet on toroidal strips, let $q$ be the Potts parameter, let $q_0(L)$ be the relevant real crossing, and let $\ell$ denote th…

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions, and let $q_{\rm c}(\mathrm{sq})=3$…

Let $q_0(L)$ denote the maximum real value in the limiting curve for a square-lattice strip of width $L$ with fully periodic boundary conditions. Odd-width square-lattice conjectur…

Let $R_c^{\texttt{NN}}(p)$ denote the critical radius for the nearest-neighbor model with parameter $p$, and let $R_c^{\texttt{dec}}$ denote the critical radius of the decorrelated…

Critical bias ratio conjecture.

For $0 \leq p \leq 1$, let $\vec{\mathbb{Z}}^2(p)$ be the random orientation of the square lattice in which each horizontal edge is oriented rightwards with probability $p$ and lef…

Let $p_{c,\mathrm{even}}$ denote the percolation threshold for Eulerian percolation on $\mathbb{Z}^2$, let $\mu_p$ be the corresponding Eulerian percolation measure, let…