自旋玻璃$\pm J$模型中Lee-Yang零点和Griffiths奇点的分布
Distribution of Lee-Yang zeros and Griffiths singularities in the $\pm J$ model of spin glasses
摘要：
本文研究了二维和三维对称$\pm J$ Ising自旋玻璃配分函数零点在复场平面上的分布。我们使用的方法来分析实现的想法，数值传递矩阵，它为我们提供了精确的表达式的配分函数作为逸度多项式。结果表明，在复场平面上，零点分布范围很广。然而，我们观察到，零的虚轴上发挥主导作用的临界行为，因为零的虚轴上是在更接近的实轴。我们估计零的密度的虚轴上的重要性抽样蒙特卡罗算法，这使我们能够采样非常罕见的事件。我们的结果表明，密度在原点有一个本质奇点。这一观察结果与本系统中存在的格里菲斯奇点是一致的。这是平衡态下自旋玻璃系统中格里菲斯奇点的第一个证据。
英文摘要：
We investigate the distribution of zeros of the partition function of the two- and three-dimensional symmetric $\pm J$ Ising spin glasses on the complex field plane. We use the method to analytically implement the idea of numerical transfer matrix which provides us with the exact expression of the partition function as a polynomial of fugacity. The results show that zeros are distributed in a wide region in the complex field plane. Nevertheless we observe that zeros on the imaginary axis play dominant roles in the critical behaviour since zeros on the imaginary axis are in closer proximity to the real axis. We estimate the density of zeros on the imaginary axis by an importance-sampling Monte Carlo algorithm, which enables us to sample very rare events. Our result suggests that the density has an essential singularity at the origin. This observation is consistent with the existence of Griffiths singularities in the present systems. This is the first evidence for Griffiths singularities in spin glass systems in equilibrium.
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