论文标题
复杂网络的隐藏几何形状和动力学：具有成对和基于三角形的互动的纳米仪器中的自旋逆转
Hidden geometry and dynamics of complex networks: Spin reversal in nanoassemblies with pairwise and triangle-based interactions
论文作者
论文摘要
对代表从大脑到社会图的复杂系统的网络的最新研究揭示了它们的高阶架构，可以由单纯骨料（三角形，四面体和更高的集团）描述。当前的研究旨在通过代数拓扑方法和深度图理论量化这些隐藏的几何形状，并了解简单复合物的动态过程。在这里，我们使用了最近引入的集团的几何自组装模型来生长三角形的纳米网络，并研究了它们上的归档驱动的自旋反转过程。随着连接到节点的伊辛旋转之间的抗磁相互作用，该组件理想地支持几何挫败感，后者被认为是凝结物理学中某些新现象的起源。在动态模型中，从成对的基于三角形相互作用的逐渐切换由参数控制。因此，旋转挫败感对每个三角形的影响让位于复杂的三角形排列条件的介观秩序。我们展示了这些相互作用之间的平衡如何改变磁滞循环的形状。同时，随附的Barkhausen噪声中的波动表现出强大的自组织关键指标，这是由网络几何形状引起的，而没有任何磁性障碍。
Recent studies of networks representing complex systems from the brain to social graphs have revealed their higher-order architecture, which can be described by aggregates of simplexes (triangles, tetrahedrons, and higher cliques). Current research aims at quantifying these hidden geometries by the algebraic topology methods and deep graph theory and understanding the dynamic processes on simplicial complexes. Here, we use the recently introduced model for geometrical self-assembly of cliques to grow nano-networks of triangles and study the filed-driven spin reversal processes on them. With the antiferromagnetic interactions between the Ising spins attached to the nodes, this assembly ideally supports the geometric frustration, which is recognized as the origin of some new phenomena in condensed matter physics. In the dynamical model, a gradual switching from the pairwise to triangle-based interactions is controlled by a parameter. Thus, the spin frustration effects on each triangle give way to the mesoscopic ordering conditioned by a complex arrangement of triangles. We show how the balance between these interactions changes the shape of the hysteresis loop. Meanwhile, the fluctuations in the accompanying Barkhausen noise exhibit robust indicators of self-organized criticality, which is induced by the network geometry alone without any magnetic disorder.
