Noise sensitivity of crossings for high temperature Ising model

Consider the event that there is a $+$ crossing from left to right in a box for the Ising model on the triangular lattice. We show that this event is noise sensitive under Glauber dynamics $t\mapsto {\sigma }_t$ in the subcritical regime $\beta <{\beta }_c$. We rely on the non-spectral approach from our previous work [TV23]. An important aspect in this more general setup is the study of the pair $({\sigma }_0,{\sigma }_t)$ and in particular the establishment of properties such as finite-energy and spatial mixing.