5 problems

Thermodynamic critical-temperature conjecture. There is a critical temperature $T_c(\lambda,\Omega)>0$ such that, for temperatures $T\geq T_c(\lambda,\Omega)$, the normal-state spi…

Global monotonicity conjecture. The map

Critical-temperature upper-bound conjecture. There is a critical temperature $T_c(\lambda,\Omega)>0$ such that, for all $\Omega>0$ and $\lambda>0$,

Graph conjecture. All $\tilde{\mathscr{C}}_c^{(N)}$ are graphs over the $\lambda$ axis for general $N\in\mathbb{N}$.

Let $H({\mathbf S}|{\mathbf N})$ be the condensation-energy functional for an admissible spin chain ${\mathbf S}$, where ${\mathbf N}$ denotes the normal-state spin chain, and let…