4 problems

Let $X(E_1,E_2,h)$ denote the number of $h$-stable configurations with normalized energy in the range $[E_1,E_2]$, where $E_1<E_2$. For $E_1,E_2,h$ such that the right-hand side be…

Let $X(E_1,E_2,h)$ denote the number of $h$-stable configurations with normalized energy in the range $[E_1,E_2]$, where $E_1<E_2$. Let the first moment entropy density be the norm…

For $h\in[-0.1,h^*)$, let $E_{cor}(h)\in\mathbb{R}$ be a candidate correlation-energy threshold, and let $W'(E,\omega,h)$ denote the function whose maximizing overlap is being stud…

Let $h^*$ denote the threshold for the existence of bisections with all vertices $h$-stable, and let the Sherrington–Kirkpatrick (SK) model be the corresponding spin-glass model. U…