论文标题
格里菲斯（Griffiths）背后的稀有区域的几何形状在随机量子磁铁中
Geometry of rare regions behind Griffiths singularities in random quantum magnets
论文作者
论文摘要
在患有淬火障碍的多体系统中，动态可观察物不仅在临界点，而且在顺磁相的扩展区域也可能是奇异的。这些格里菲斯的奇异性是由于稀有区域造成的，这些区域在有序阶段局部，并有助于较大的敏感性。在这里，我们研究具有稀释度或随机耦合和横向场的横向iSing模型中稀有区域的几何特性。在稀释的模型中，罕见的区域是渗透簇，而在随机模型中，基态由一组自旋簇组成，这些簇由强障碍重新归化方法计算得出。我们认为所谓的能量群集，其具有最小的激发能，并计算其在一，二维和三维中的质量和线性延伸。发现两个平均数量与样品的线性大小对数生长。因此，稀有区域不是紧凑的：对于稀释的模型，它们是各向同性和树状的，而对于随机模型，它们是准二维的。
In many-body systems with quenched disorder, dynamical observables can be singular not only at the critical point, but in an extended region of the paramagnetic phase as well. These Griffiths singularities are due to rare regions, which are locally in the ordered phase and contribute to a large susceptibility. Here, we study the geometrical properties of rare regions in the transverse Ising model with dilution or with random couplings and transverse fields. In diluted models, the rare regions are percolation clusters, while in random models the ground state consists of a set of spin clusters, which are calculated by the strong disorder renormalization method. We consider the so called energy cluster, which has the smallest excitation energy and calculate its mass and linear extension in one-, two- and three-dimensions. Both average quantities are found to grow logarithmically with the linear size of the sample. Consequently, the rare regions are not compact: for the diluted model they are isotropic and tree-like, while for the random model they are quasi-one-dimensional.
