Cutoff for the Ising model throughout the rapidly-mixing regime on bounded-degree graphs

Establish total-variation cutoff for the Gibbs sampler (single-site update chain) of the Ising model on bounded-degree graphs throughout the entire rapidly-mixing regime (e.g., the tree uniqueness regime).

Background

Information Percolation proves cutoff for the Ising model at high temperature (strong spatial mixing) on lattices, but it requires strong decoupling and does not apply across the entire rapidly-mixing regime. Recent progress via spectral independence and entropy factorization shows rapid mixing throughout the tree uniqueness regime; the conjecture is that cutoff should also hold there.