PHASE TRANSITIONS AND EXCITATIONS IN FRACTAL MAGNETS

一般认为，渗透团簇的原子连通性采用分形的形式。渗透理论是由许多作者提出的，现在可以用来解释各种各样的物理和化学现象，如凝胶过程、非晶材料中的输运和掺杂半导体中的跳跃传导。分形的概念对渗透的理解做出了重大贡献。最简单的理想渗透网络是通过用非磁性原子代替稀释磁性体系来实现的。在临界磁浓度（c_p）下，单个无限簇（一个渗透网络）横跨整个空间；随着磁性原子浓度的进一步降低，系统分裂成只有有限簇的集合。渗透网络表现出自相似性，可以用非整数质量维来表征，即分形维数D_f。在方形晶格中，通过数值估计，渗透网络的D_f为1.896，即D_f小于欧几里得维数d。众所周知，中子散射是研究磁系统静态和动态方面的有力工具。通过观测自旋对相关函数的时空傅里叶变换——散射函数，我们可以得到这些系统的结构和动力学性质的详细信息。在本研究中，我们成功地在二维和三维渗透反铁磁体中进行了中子散射实验；对渗透团簇中磁序自相似性的直接观察，对具有伊辛对称的渗透反铁磁体中磁激发的研究，对渗透海森堡反铁磁体中分形的观察，以及对渗透海森堡反铁磁体中反常自旋扩散的观察

It is generally accepted that the atomic connectivity of a percolating cluster takes the form of a fractal. The theory of percolation was formulated by many authors and can now be used to interpret an exceptionally wide variety of physical and chemical phenomena, such as the gelation process, transport in amorphous materials, and hoppoing conduction in a doped semiconductor. The concept of fractals has contributed significantly to the understanding of percolation. The simplest ideal percolating networks are realized by substitutionaly diluting the magnetic systems by non-magnetic atoms. At a critical magnetic concentration (c_p), a single infinite cluster (a percolating network) spans the full space ; with a further decreasing concentration of magnetic atoms, the system splits into an assembly of only finite clusters. The percolating networks exhibit a self-similarity, and can be characterized by a non-integer mass dimension, i. e., a fractal dimension D_f. In a square lattice, it has been numerically estimated that the D_f of the percolating network is 1.896, i.e. D_f is less than the Euclidian dimension, D.As is well established, neutron scattering is a powerful tool to investigate the static and dynamical aspects of magnetic systems. By observing the scattered scattering function that is the space-time Fourier transform of the spin pair-correlation function, we can obtain the detailed information concerning the structural and dynamical properties of these systems. In the present research, we successfully performed neutron scattering experiments in two-and three-dimensional percolating antiferromagnets ; a direct observation of the self-similarity of the magnetic order in a percolating cluster, investigations of the magnetic excitations in percolating antiferromagnets with Ising symmetry, an observation of fractons in a percolating Heisenberg antiferromagnet and an observation of anomalous spin diffusion in a percolating Heisenberg ant