论文标题
ISING模型分区功能计算作为加权计数问题
Ising Model Partition Function Computation as a Weighted Counting Problem
论文作者
论文摘要
尽管Ising模型对于了解物理现象仍然至关重要，但其与组合推理的自然联系也使其也是探测科学和工程中复杂系统的最佳模型之一。我们为Ising模型的研究带来了计算镜头，我们的计算机科学观点是两个方面：一方面，我们考虑了ISING分区功能问题的计算复杂性或#isising的计算复杂性，并将其与基于逻辑的约束 - 满意度问题计数相关联。我们表明，#CSP的已知二分法结果简单地证明了#Sising的硬度，并提供了有关#Sising难度来自何处的新直觉。另一方面，我们还表明#isis可以简化为加权模型计数（WMC）。这使我们能够采用现成的模型计数器并将其应用于#ising。我们表明，这种WMC方法的表现优于#ising的最先进的专业工具，从而扩大了计算物理中可解决的问题的范围。
While the Ising model remains essential to understand physical phenomena, its natural connection to combinatorial reasoning makes it also one of the best models to probe complex systems in science and engineering. We bring a computational lens to the study of Ising models, where our computer-science perspective is two-fold: On the one hand, we consider the computational complexity of the Ising partition-function problem, or #Ising, and relate it to the logic-based counting of constraint-satisfaction problems, or #CSP. We show that known dichotomy results for #CSP give an easy proof of the hardness of #Ising and provide new intuition on where the difficulty of #Ising comes from. On the other hand, we also show that #Ising can be reduced to Weighted Model Counting (WMC). This enables us to take off-the-shelf model counters and apply them to #Ising. We show that this WMC approach outperforms state-of-the-art specialized tools for #Ising, thereby expanding the range of solvable problems in computational physics.
