9 problems

Gibbs-measure existence conjecture. The family

Untempered-limit conjecture. Untempered thermodynamic limits should exist even for

Symmetry-breaking phase conjecture. For $\alpha=0$, outside the class of measures without infinite contours, there exists an infinite number of extreme infinite-volume phases break…

Consider a sequence of finite regions converging to a fixed shape, and let $(s,t)$ be the tilt given by the variational principle wherever that tilt is defined. Let $\mu_{s,t}$ be…

Let $(s,t)$ satisfy $|s|+|t| \leq 2$, and let $a,b,c,d$ be weights satisfying $ab=cd$ such that the average height function for weighted torus tilings has tilt $(s,t)$. Let…

Thermodynamic-limit independence conjecture. The final results—the energy per unit cell and the ground-state density of the crystal—should not depend on the chosen thermodynamic-li…

A spin glass model is considered with symmetric boundary conditions, and its finite-volume Gibbs measures are studied as the volume tends to infinity. Newman–Stein's conjecture. So…

Let $f(t)$ be the subsequential thermodynamic limit of the transverse magnetization observable in the Edwards–Anderson spin-glass model, as in equation (31), along a subsequence…

High-density ground-state and infinite-density ground-state conjecture. If $u$ is superstable and strongly tempered, then high-density GSCs and IDGSs in infinite space exist. Every…