1993 Fiscal Year Final Research Report Summary
PHASE TRANSITIONS AND EXCITATIONS IN FRACTAL MAGNETS
| Project/Area Number |
03402009
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| Research Category |
Grant-in-Aid for General Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS |
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Principal Investigator |
IKEDA Hironobu NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS, BSF, PROF., ブースター利用施設, 教授 (90013523)
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| Co-Investigator(Kenkyū-buntansha) |
ARAI Matatoshi NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS, BSF, ASSOC.PROF., 理学部, 助教授 (30175955)
FURUSAKA Michihiro NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS, BSF, ASSOC.PROF., ブースター利用施設, 助教授 (60156966)
IKEDA Susumu NATIONAL LABORATORY FOR HIGH ENERGY PHYSICS, BSF, ASSOC.PROF., ブースター利用施設, 助教授 (80132679)
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| Project Period (FY) |
1991 – 1993
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| Keywords | PERCOLATION / FRACTAL / FRACTON / FRACTAL DIMENSION / NEUTRON SCATTERING / ANOMALOUS DIFFUSION / DILUTE MAGNET |
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| Research Abstract |
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
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