准高斯态密度的Fisher零点
Fisher's zeros of quasi-Gaussian densities of states
摘要：
我们讨论了四维纯SU（2）格点规范理论的配分函数在复$β$平面上的零点（Fisher零点）的位置的明显矛盾。我们提出了一个新的标准来绘制复$β$平面的区域，当态密度几乎但不完全是高斯时，可以信任重加权方法。我们提出了新的方法来推断这个区域以外的零的存在。我们证明了这些建议的可靠性与准高斯蒙特卡罗分布的零点的位置可以通过独立的数值方法计算。结果表明，该方法可以应用于一般的晶格模型。具体的晶格模型的应用将在单独的出版物中讨论。
英文摘要：
We discuss apparent paradoxes regarding the location of the zeros of the partition function in the complex $β$ plane (Fisher's zeros) of a pure SU(2) lattice gauge theory in 4 dimensions. We propose a new criterion to draw the region of the complex $β$ plane where reweighting methods can be trusted when the density of states is almost but not exactly Gaussian. We propose new methods to infer the existence of zeros outside of this region. We demonstrate the reliability of these proposals with quasi Gaussian Monte Carlo distributions where the locations of the zeros can be calculated by independent numerical methods. The results are presented in such way that the methods can be applied for general lattice models. Applications to specific lattice models will be discussed in a separate publication.
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