Polynomial-time approximation algorithms for the antiferromagnetic Ising model on line graphs

关于反铁磁Ising模型的占据分数

On the occupancy fraction of the antiferromagnetic Ising model

本文研究正则图中反铁磁Ising模型的最大和最小占据分数，确定了Δ=3时近似采样复杂度计算阈值，并指出方法向更大Δ扩展的挑战。

Approximating Pairwise Correlations in the Ising Model

In the Ising model, we consider the problem of estimating the covariance of the spins at two specified vertices. In the ferromagnetic case, it is easy to obtain an additive approximation to this covariance by repeatedly sampling from the relevant Gibbs distribution. However, we desire a multiplicative approximation, and it is not clear how to achieve this by sampling, given that the covariance can be exponentially small. Our main contribution is a fully polynomial time randomised approximation scheme (FPRAS) for the covariance. We also show that that the restriction to the ferromagnetic case i…

随机正则二分图上反铁磁伊辛模型的完全多项式随机近似方案

An FPRAS for Antiferromagnetic Ising Models on Random Regular Bipartite Graphs

该研究针对随机正则二分图上带均匀外场的反铁磁伊辛模型配分函数，推广硬核模型的近似方法，在特定参数条件下提出带截断的吉布斯采样算法，实现高效近似并证明其高概率性。

Lower bounds for testing graphical models: colorings and antiferromagnetic Ising models

We study the identity testing problem in the context of spin systems or undirected graphical models, where it takes the following form: given the parameter specification of the model $M$ and a sampling oracle for the distribution $μ_{\hat{M}}$ of an unknown model $\hat{M}$, can we efficiently determine if the two models $M$ and $\hat{M}$ are the same? We consider identity testing for both soft-constraint and hard-constraint systems. In particular, we prove hardness results in two prototypical cases, the Ising model and proper colorings, and explore whether identity testing is any easier than s…