论文标题
在二维Ising自旋玻璃中的簇渗透
Cluster Percolation in the Two-Dimensional Ising Spin Glass
论文作者
论文摘要
合适的集群定义使研究人员可以将自旋系统中的许多有序转变描述为与渗透有关的几何现象。但是，对于旋转玻璃和一些具有猝灭障碍的系统，这种连接尚未完全建立，数值证据仍然不完整。在这里，我们使用Monte Carlo模拟来研究Edwards-Anderson Ising Spining玻璃模型中出现的几类簇的渗滤特性。最初针对铁磁问题定义的fortuin-kasteleyn-coniglio-klein群集在热力学极限下始终在温度下进行渗透。在Nishimori线上，由于Yamaguchi引起的参数，该位置准确地预测了该位置。与自旋玻璃过渡更相关的是根据几个复制品的重叠定义的簇。我们表明，各种此类簇类型具有渗透阈值，通过增加系统大小将其转移到较低的温度，这与零温度的自旋玻璃玻璃转变一致。重叠与两个最大簇的密度差有关，从而支撑了旋转玻璃过渡对应于渗透阶段内两个最大簇的新兴密度差。
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn-Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains non-zero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperature by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.
