CM
In the literature: open
Do dynamical transition times coincide with zeros of the order parameter
In plain words
In some models the kinks happen exactly when the measured order of the system passes through zero, in others they do not. When the two coincide is unknown.
Precise statement
For quenches from a symmetry-broken state, determine the conditions under which the nonanalytic times $t_c$ of the Loschmidt rate $l(t)$ coincide with zeros or sign changes of the order-parameter expectation value $m(t)$. Answer: a criterion valid for interacting models in $d = 1 \text{ and } 2$.
What would settle it
A criterion proved, or verified numerically across interacting models in $d = 1\text{ and }2$, including cases with and without coincidence.