巡游电子铁磁性的非广延量子方法：分形化方法
Nonextensive quantum method for itinerant-electron ferromagnetism: Fractorization approach
摘要：
本文用非广延量子系统的广义费米-狄拉克分布讨论了哈伯德模型描述的巡游电子（金属）铁磁体的磁性和磁性。我们导出了超统计量中的GFD分布，它等价于用最大熵方法得到的Tsallis熵的因子分解近似。本文用Hartree-Fock近似计算了哈伯德模型中电子-电子相互作用的磁矩、能量、比热和Curie-Weiss型自旋磁化率随温度和熵指数$q$的变化关系：$q=1.0$对应于Boltzmann-Gibbs统计。结果表明，随着$| q-1 |$非外延性的增加，磁矩的温度依赖性变得更加显著，低温电子比热也大大增加。这是由于放大的斯通纳激发的GFD分布，这是阐明了与使用广义索末菲展开的分析。讨论了非伸缩性对金属铁磁体和绝缘铁磁体影响的异同。
英文摘要：
Magnetic and thermodynamical properties of itinerant-electron (metallic) ferromagnets described by the Hubbard model have been discussed with the use of the generalized Fermi-Dirac (GFD) distribution for nonextensive quantum systems. We have derived the GFD distribution within the superstatistics, which is equivalent to that obtained by the maximum-entropy method to the Tsallis entropy with the factorization approimation. By using the Hartree-Fock approximation to the electron-electron interaction in the Hubbard model, we have calculated magnetic moment, energy, specific heat and Curie-Weiss-type spin susceptibility, as functions of the temperature and entropic index $q$ expressing the degree of the nonextensivity: $q=1.0$ corresponds to the Boltzmann-Gibbs statistics. It has been shown that with increasing the nonextensivity of $| q-1 |$, the temperature dependence of magnetic moment becomes more significant and the low-temperature electronic specific heat is much increased. This is attributed to enlarged Stoner excitations in the GFD distribution, which is elucidated by an analysis with the use of the generalized Sommerfeld expansion. We discuss the difference and similarity between the effects of the nonextensivity on metallic and insulating ferromagnets.
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