We give a near-linear time sampler for the Gibbs distribution of the ferromagnetic Ising models with edge activities $\boldsymbol{\beta} > 1$ and external fields $\boldsymbol{\lambda}<1$ (or symmetrically, $\boldsymbol{\lambda}>1$) 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.

翻译：我们提出了一种近乎线性时间的采样器，用于边活性参数 $\boldsymbol{\beta} > 1$、外场 $\boldsymbol{\lambda}<1$（或对称地，$\boldsymbol{\lambda}>1$）的铁磁伊辛模型在具有有界或无界最大度的一般图上的吉布斯分布。我们的算法基于[CFYZ21]中给出的场动力学。我们通过建立随机团簇模型分布的谱独立性以及低温区域中随机团簇模型上格劳伯动力学的快速混合来证明我们算法的正确性和效率，这些结果可能具有独立的意义。