论文标题
旋转冰图的概念及其拓扑单孔和电荷的现场理论
The Concept of Spin Ice Graphs and a Field Theory for their Topological Monopoles and Charges
论文作者
论文摘要
现在可以在控制其集体行为和异国特性的各种几何形状中捏造自旋冰。因此，它们的正确框架是图理论。我们将旋转冰概念（例如冰规则，冰歧管，库仑相，指控和单孔）与图理论概念（例如平衡，内/超级和欧拉尔里亚语）相关联。然后，我们提出了一种现场理论治疗，其中拓扑电荷和单孔是自由度，而二元旋转则归入了电荷之间的熵相互作用。我们表明，对于高斯近似中图上的旋转冰，熵相互作用的内核是图laplacian的倒数，并且我们从图形上计算出图中的筛选函数，作为图形上筛选的泊松问题的绿色操作员。然后，我们将治疗方法应用于不同维度的星形图，比赛，周期和常规旋转冰。
Spin ices can now be fabricated in a variety of geometries which control their collective behavior and exotic properties. Therefore, their proper framework is graph theory. We relate spin ice notions such as ice rule, ice manifold, Coulomb phases, charges and monopoles, to graph-theoretical notions, such as balance, in/out-degrees, and Eulerianicity. We then propose a field-theoretical treatment in which topological charges and monopoles are the degrees of freedom while the binary spins are subsumed into entropic interaction among charges. We show that for a spin ice on a graph in a Gaussian approximation, the kernel of the entropic interaction is the inverse of the graph Laplacian, and we compute screening functions from the graph spectra as Green operators for the screened Poisson problem on a graph. We then apply the treatment on star graphs, tournaments, cycles, and regular spin ice in different dimensions.
