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arXiv · 2609.26197

An $\widetilde{O}\left(n^2 \right)$-Time Sampler for Zero-Field Ferromagnetic Ising Models

Weiming Feng·Heng Guo·Yiyao Zhang
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Abstract

We give an approximate sampler for ferromagnetic Ising models with no field on arbitrary graphs that runs in time $\widetilde O(m+n)+\widetilde O_β(n^2\log^2 (1 / \varepsilon))$, where $n$ and $m$ are the numbers of vertices and edges, respectively, and $\varepsilon$ is the approximation error. Our approach combines Benczúr--Karger cut sparsification with a new mixing time analysis of the Glauber dynamics for the random-cluster model. The mixing time analysis features a new monotone edge-count Poincaré inequality.

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Weiming Feng, Heng Guo, Yiyao Zhang. 2026-09-23. An $\widetilde{O}\left(n^2 \right)$-Time Sampler for Zero-Field Ferromagnetic Ising Models. https://arxiv.org/abs/2609.26197

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