发帖
雷达卡
摘要翻译：
本文研究了二维和三维对称的$\PMJ$Ising自旋玻璃配分函数零点在复场平面上的分布。我们用该方法解析地实现了数值传递矩阵的思想，给出了配分函数作为逸度多项式的精确表达式。结果表明，在复场平面内零点分布在很宽的区域内。然而，我们观察到虚轴上的零点在临界行为中起主导作用，因为虚轴上的零点更接近实轴。我们用一种重要抽样蒙特卡罗算法来估计虚轴上零点的密度，这使得我们能够对非常罕见的事件进行抽样。我们的结果表明，密度在原点有一个本质的奇异性。这一观察结果与目前系统中Griffiths奇点的存在是一致的。这是平衡态自旋玻璃系统中Griffiths奇点的第一个证据。
---
英文标题：
《Distribution of Lee-Yang zeros and Griffiths singularities in the $\pm
J$ model of spin glasses》
---
作者：
Yoshiki Matsuda, Hidetoshi Nishimori, Koji Hukushima
---
最新提交年份：
2008
---
分类信息：
一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
--
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--
---
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.
---
PDF链接：
https://arxiv.org/pdf/712.4063
京公网安备 11010802022788号
