3 problems

Synchronization threshold conjecture. There exists a function $\psi:[0,\infty)\to[0,\infty)$ such that synchronization occurs if and only if

Let $d\geq 1$ and let $\beta\in[0,\beta_c(d))$, where $\beta_c(d)$ is the critical inverse temperature of the classical Ising model on $\mathbb{Z}^d$. Consider the Ising model pert…

Let $t$ denote time, and let $m'$ be a final magnetization. A value of $m'$ is called bad when the corresponding time-evolved potential has competing global minima, causing non-Gib…