Noise sensitivity of crossings for high temperature Ising model

TL;DR

This paper demonstrates that the occurrence of a specific crossing event in the high temperature Ising model on a triangular lattice is highly sensitive to small perturbations over time, using a non-spectral approach.

Contribution

It extends noise sensitivity analysis to the high temperature Ising model under Glauber dynamics, emphasizing properties like finite-energy and spatial mixing.

Findings

Crossing events are noise sensitive in the subcritical regime.

The non-spectral approach is effective for this analysis.

Properties like finite-energy and spatial mixing are established.

Abstract

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.