铁磁Potts模型配分函数的近似
Approximating the partition function of the ferromagnetic Potts model
摘要：
我们提供的证据表明，它是计算上难以近似的铁磁q态Potts模型的配分函数时，q>2。具体来说，我们证明了分区函数是困难的复杂性类#RHPi_1下近似保持约简。因此，它是很难近似的分区函数，因为它是找到近似的解决方案，以广泛的计数问题，包括确定的数目，独立集在一个二分图。我们的证明利用了“随机簇”模型的一阶相变，这是一个概率分布图，是密切相关的q状态波茨模型。
英文摘要：
We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1 under approximation-preserving reducibility. Thus, it is as hard to approximate the partition function as it is to find approximate solutions to a wide range of counting problems, including that of determining the number of independent sets in a bipartite graph. Our proof exploits the first order phase transition of the "random cluster" model, which is a probability distribution on graphs that is closely related to the q-state Potts model.
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