Research Paper#Statistical Physics, Markov Chain Monte Carlo, Ising Model, Mixing Time🔬 ResearchAnalyzed: Jan 3, 2026 19:34
Fast Mixing in Ising Models with Negative Spectral Outlier
Published:Dec 28, 2025 06:28
•1 min read
•ArXiv
Analysis
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.
Key Takeaways
Reference
“The paper develops a new covariance approximation method based on Gaussian approximation, implemented via an iterative application of Stein's method.”