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

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