5 problems

Fix $k\in\mathbb{N}$. For the Ising partition function $Z_{\mathbb{Z}_m^t}(\lambda,\beta)$ on the even torus $\mathbb{Z}_m^t$, let $L_j$ denote the sum of the weights of clusters o…

Modified scaling conjecture. The limits obtained using $E_1$, $E_2$, or $E$ are equal and satisfy

Modified cluster-expansion limit conjecture. Using $E_1$, $E_2$, or $E$, the following limit exists:

Universal-limit conjecture. The limits obtained using $E_1$, $E_2$, or $E$ are equal, and

Ruelle-potential decomposition conjecture. Any stable and tempered pair potential can always be written as a sum of a non-negative potential plus an absolutely summable stable pote…