论文标题
Swendsen-Wang动力学用于具有外部字段的铁磁ising模型
Swendsen-Wang dynamics for the ferromagnetic Ising model with external fields
论文作者
论文摘要
我们研究了具有一致的外部场，尤其是该模型上的Swendsen-Wang动力学的铁磁ising模型的采样问题。我们介绍了一个新的大型模型，统一了两个密切相关的模型：子图世界和随机群集模型。通过这种新的观点，我们显示：（1）随机群集模型的Swendsen-Wang动力学和（边缘悬挂）Glauber动力学的多项式混合时间边界，从而概括了边界并简化了Guo和Jerrum（2018）的否场情况的证明； （2）如果最大程度界限，并且所有字段均（一致且）远离$ 1 $，则在上述两个动力学的线性混合时间附近。
We study the sampling problem for the ferromagnetic Ising model with consistent external fields, and in particular, Swendsen-Wang dynamics on this model. We introduce a new grand model unifying two closely related models: the subgraph world and the random cluster model. Through this new viewpoint, we show: (1) polynomial mixing time bounds for Swendsen-Wang dynamics and (edge-flipping) Glauber dynamics of the random cluster model, generalising the bounds and simplifying the proofs for the no-field case by Guo and Jerrum (2018); (2) near linear mixing time for the two dynamics above if the maximum degree is bounded and all fields are (consistent and) bounded away from $1$.
