Fast Mixing in Ising Models with Negative Spectral Outlier

This paper addresses the challenge of analyzing the mixing time of Glauber dynamics for Ising models when the interaction matrix has a negative spectral outlier, a situation where existing methods often fail. The authors introduce a novel Gaussian approximation method, leveraging Stein's method, to control the correlation structure and derive near-optimal mixing time bounds. They also provide lower bounds on mixing time for specific anti-ferromagnetic Ising models.