14 problems

Let $G$ range over the family of subgraphs of the square lattice considered by Matt Blum, and let $u(G)$ denote the number of perfect matchings of $G$. Blum's conjecture. For…

Let $E_L$ and $C_L$ denote the finite-size correction quantities introduced in the source for strips of width $L$, for both the square and triangular lattices. Vanishing-correction…

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 $q_0(L)$ be the crossing value for an even-width square-lattice strip, with finite-size behavior fitted by $q_0(L)=q_{\rm c}(\mathrm{sq})+A L^{-1/\nu}$. Square-lattice exponent…

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…

Consider the complete-neighbor and nearest-neighbor models in their super-critical regimes, where an infinite connected component exists with positive probability. Infinite-cluster…

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.

The $\mathbb{Z}^2$ critical exponent conjecture. The exponent is

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…

Van den Berg–Brouwer conjecture. There exists a constant $c>0$ such that

Antiferromagnetic-ray conjecture. In the limit of an infinitely large basis, $P_B(q,v)$ contains this square-lattice factor and a remaining factor whose zeros produce two vertical…