铁磁双自旋系统的零点

作者：Heng Guo,Jingcheng Liu,Pinyan Lu

摘要：我们根据外场研究了铁磁2-态自旋系统的分配函数的零点，并通过Asano和Ruelle的收缩方法的细化来获得这些系统的新的零自由区域。 我们的结果的强度是它们不依赖于底层图的最大程度。 通过Barvinok的方法，我们还获得了新的有效和确定性的近似计数算法。 在某些制度中，我们的算法优于所有其他方法，如马尔可夫链蒙特卡罗和相关衰减。

原文标题：Zeros of ferromagnetic 2-spin systems

原文摘要：We study zeros of the partition functions of ferromagnetic 2-state spin systems in terms of the external field, and obtain new zero-free regions of these systems via a refinement of Asano's and Ruelle's contraction method. The strength of our results is that they do not depend on the maximum degree of the underlying graph. Via Barvinok's method, we also obtain new efficient and deterministic approximate counting algorithms. In certain regimes, our algorithm outperforms all other methods such as Markov chain Monte Carlo and correlation decay.

地址：https://arxiv.org/abs/1907.06156