How magnetism will change when the dimension of sample changes

本课题旨在通过实验数据阐明磁跃迁、超导跃迁等协同现象中分形维数(D)与有序的关系。本研究的新颖之处在于实现了对给定样品的D的控制，并阐明了它们的电子性质。三年来，这项研究已达到了大部分目的。以下是通过测量不同分形维数的样品的物理性质而得到澄清的；CoO的尼尔温度与其分维数的关系，以及高t_c氧化铜超导体的临界电流密度与其分维数的关系。这些结果在申请专利后发表在科学期刊上。

The purpose of this research project is to clarify the relationship between fractal dimension (D) and ordering in cooperative phenomena such as magnetic and superconducting transitions by presenting experimental data. The novelty of this research lies in the realization of control of D of given samples and elucidation of their electronic properties. For three years the study has achieved most of the purposes. The followings have been clarified by measurements of the physical properties of samples with various farctal dimensions; the relationship between Neel temperature of CoO and its fractal dimension, and that between critical current density of high-T_C copper oxide superconductors and its fractal dimension. These results are published in scientific journals after patent was applied.