12 problems

Let $q_2(L)$ denote the crossing of the two largest eigenvalues in the $\ell=2$ sector for a triangular-lattice strip of width $L$ with fully periodic boundary conditions, and let…

Let $q_0(L)$ denote the crossing for a triangular-lattice strip of width $L$ with fully periodic boundary conditions, and let $q_{\rm B}\simeq3.8196717312$ be the value where Baxte…

Consider the $|\varphi|^4$ model with free boundary conditions (FBC), and let $\chi_{g,\nu,N}^{\rm F}$ denote its susceptibility, while $\chi_{g,\nu,N}$ denotes the susceptibility…

Let $\operatorname{\bf NG}_{s}$ be the probability measure whose moment generating function is specified by … Under the assumptions of Theorem, let $w_N$ denote the critical-window…

Pseudocritical-profile conjecture. For $d>d_{\mathrm{c},\alpha}$, there is a pseudocritical point

Table-profile conjecture. The profile functions $f(s)$ are the functions listed in Table for both SR and LR models in every dimension $d\ge d_{\mathrm{c},\alpha}$, including the up…

Universal-profile conjecture. The preceding susceptibility and two-point-function asymptotics hold for every listed model, with the same profile function for its SR and LR versions…

Percolation scaling-profile conjecture. There exist constants $a,b>0$ such that, as $V\to\infty$,

Lattice-tree and lattice-animal profile conjecture. The same critical finite-size scaling profile $I_0$ occurs for both lattice trees and lattice animals on $\mathbb{T}_r^d$ above…

Let $W^*$ be the Brownian excursion of length $1$, let $\Psi(x)=\mathbb{E}\exp\left[x\int_0^1W^*(t)\,\mathrm dt\right]$ be the moment-generating function of its area, and define ……

Free-boundary effective critical point conjecture. There exists such a $\beta_{c,r}$ for which all statements of the non-Gaussian limit and universal profile conjecture hold with…

Non-gaussian limit and universal profile conjecture. As $r\to\infty$, $h_r^{-1}S_r$ converges in distribution under $\langle\cdot\rangle_{\beta_c+sw_r}^{\mathbb{T}_r}$ to…