论文标题
具有外场的Ising模型的接近线性时间采样器
A Near-Linear Time Sampler for the Ising Model with External Field
论文作者
论文摘要
我们给出了一个接近线性的时间采样器，用于具有边缘活动$ \boldsymbolβ> 1 $和外部字段的吉布斯分布$ \boldsymbolλ<1 $ <1 $（或对称性，$ \boldsymbolλ> 1 $）。 我们的算法基于[CFYZ21]中给出的场动力学。我们通过建立随机群集模型的分布的光谱独立性以及在低温方向上的随机聚类模型上快速混合Glauber动力学的快速混合，从而证明了我们的算法的正确性和效率，这可能具有独立的利益。
We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities $\boldsymbolβ > 1$ and external fields $\boldsymbolλ<1$ (or symmetrically, $\boldsymbolλ>1$) on general graphs with bounded or unbounded maximum degree. Our algorithm is based on the field dynamics given in [CFYZ21]. We prove the correctness and efficiency of our algorithm by establishing spectral independence of distribution of the random cluster model and the rapid mixing of Glauber dynamics on the random cluster model in a low-temperature regime, which may be of independent interest.
