6 problems

Fix a maximum degree $d$. Let $(G_n)_{n\geq1}$ be a sequence of finite connected graphs, with $G_n=(V_n,E_n)$, $|V_n|\to\infty$, and maximum degree at most $d$. The polylogarithmic…

Let $\chi(\beta)$ denote the susceptibility of the high-dimensional Ising model and let $\beta_c$ be its critical inverse temperature. Logarithmic susceptibility conjecture. Let…

Truncated susceptibility conjecture. This quantity is finite for every $p_c<p\leq1$.

Vanishing modified susceptibility conjecture. The modified susceptibility satisfies

Let $\kappa$ be an irreducible kernel, let $\widehat\chi(\lambda\kappa)$ denote the dual susceptibility, and let $\lambda_{\mathrm{cr}}$ be the critical parameter. Analyticity and…

Let $\tilde{\chi}^{(n)}$ denote the $n$-particle contribution to the square-lattice Ising susceptibility, and let $k$ range over the lower-index contributions appearing as…