Susceptibility threshold conjecture for anisotropic bond percolation

Consider an anisotropic bond percolation process on ${\mathbb {Z}}^d\times{\mathbb {Z}}^s$, with $d,s\geq1$, parameters $(p,q)$, and $p_c(d)-p>0$ sufficiently small. Let $\chi_p(d)$ denote the susceptibility of the $d$-dimensional process. Susceptibility threshold conjecture. There exists a constant $\beta$ such that, whenever

$$q>\frac{\beta}{\chi_p(d)},$$

the pair $(p,q)$ gives, almost surely, an infinite open cluster in ${\mathbb {Z}}^{d+s}$. This conjectured bound would connect the onset of percolation in the higher-dimensional anisotropic model to the susceptibility of the lower-dimensional model; the source states that it is expected to hold for all $d$.