Information percolation and cutoff for the stochastic Ising model (Q2802070)

The authors study Glauber dynamics for the Ising model on \((\mathbb{Z}/n\mathbb{Z})^d\) using a new technique which they call ``information percolation''. They use this technique to show that, for large \(n\), continuous-time Glauber dynamics exhibit the cutoff phenomenon both above the critical temperature and below the critical temperature in the presence of a non-zero magnetic field, thus settling a conjecture of \textit{Y. Peres} [\textit{D. A. Levin} et al., Probab. Theory Relat. Fields 146, No. 1--2, 223--265 (2010; Zbl 1187.82076), Conjecture 1]. They also consider the question of how the mixing time is affected by the initial configuration. In particular, they show that the mixing time in the case of a uniformly distributed initial condition is half that of the all-plus initial condition. These results are a considerable improvement on the existing literature.NEWLINENEWLINE(A complete description of information percolation is beyond the scope of this review, but we refer to Section 1.2 of the paper, where the physical intuition behind this concept is clearly explained.)