发表机构
School of Computer Science and Technology, University of Science and Technology of China; School of Computing and Data Science, The University of Hong Kong（中国科学技术大学计算机科学与技术学院; 香港大学计算与数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对同一有界度图上自旋系统诱导的吉布斯分布间的总变差距离，研究其确定性相对近似，针对硬核模型和伊辛模型分别给出确定性多项式时间近似算法，提出将该任务归约为估计合适配分函数的新确定性框架。
AI 中文摘要
我们研究同一有界度图上自旋系统诱导的两个吉布斯分布间总变差距离的确定性相对近似。对于硬核模型，当两个外场向量均位于$[b,(1-\eta)\lambda_{\mathrm c}(\Delta)]^V$中时，我们给出确定性多项式时间$\varepsilon$相对误差近似，其中$b>0$和$\eta\in(0,1)$是固定的，$\lambda_{\mathrm c}(\Delta)$为硬核唯一性阈值。对于伊辛模型，我们在两种场景中得到确定性多项式时间算法：铁磁Lee–Yang regime和反铁磁关联衰减 regime。我们开发了一种新的确定性框架，将该任务归约为估计合适的配分函数。
英文摘要
We study deterministic relative approximation of the total variation distance between two Gibbs distributions induced by spin systems on the same bounded-degree graph. For the hard-core model, we give a deterministic polynomial-time $\varepsilon$-relative-error approximation when both external-field vectors lie in $[b,(1-η)λ_{\mathrm c}(Δ)]^V$, where $b>0$ and $η\in(0,1)$ are fixed and $λ_{\mathrm c}(Δ)$ is the hard-core uniqueness threshold. For the Ising model, we obtain deterministic polynomial-time algorithms in two settings: the ferromagnetic Lee--Yang regime and the antiferromagnetic correlation-decay regime. We develop a new deterministic framework that reduces this task to estimating suitably chosen partition functions.
