3 problems

Iagolnitzer–Souillard conjecture. This asymptotic behavior should hold whenever $h\neq 0$.

Consider the ferromagnetic long-range Ising model on $\mathbb{Z}^d$, with $d\geq 2$, coupling $J_{xy}=J|x-y|^{-\alpha}$ for $J>0$ and $\alpha>d$, and a decaying magnetic field of t…

Equality conjecture. For the relevant values of $\alpha$, the one-sided and two-sided critical inverse temperatures are equal: