Frustrated Magnetism and Chiral Order

手性是一种自由度，表示有序状态的局部结构的感觉或惯用手。在分子化学领域，它一直是与分子立体异构体问题联系在一起的一个重要概念。最近，通过最近的活跃研究，人们越来越清楚手性在统计物理和凝聚态物理领域中的各种材料中也起着至关重要的作用。这个项目的目的是通过大量的数值模拟从理论上阐明手性有序的本质。更具体地说，我们讨论了自旋玻璃问题以及几何受挫磁铁问题。在海森堡自旋玻璃的非平衡动力学和涨落耗散比，类海森堡自旋玻璃在磁场中的有序性，反常霍尔效应作为自旋玻璃手征有序性的探针和对实验的标度预测等方面取得了进展。所得结果与自旋-玻璃跃迁的手性理论相一致，并得到了近期实验的支持。特别是，使用霍尔探测器检测手征有序可能会在凝聚态物理学中开辟一个新的领域。我们还在如下问题中发现了几个新的有序性质：(Iv)焦绿石晶格上海森堡反铁磁体的磁性有序。

Chirality is a degree of freedom representing the sense or the handedness of the local structure of the ordered state. In the field of molecular chemistry, it has long been an important concept in conjunction with the problem of stereo-isomer of a molecule. Recently, via recent active studies, it has become increasing clear that the chirality also plays a vital role in various materials in the field of statistical physics and condensed matter physics. This project was performed with the aim of theoretically clarifying the nature of the chirality ordering by using extensive numerical simulations. More specifically, we took up the spin-glass problem as well as the problem of geometrically frustrated magnets. Progress was achieved in the particular issues of, (I) off-equilibrium dynamics and the fluctuation-dissipation ratio of the Heisenberg spin glass, (II) ordering of Heisenberg-like spin glasses in magnetic fields, and (III) anomalous Hall effect as a probe of the chiral order in spin glasses and a scaling prediction to the experiment. The obtained results are consistent with the chirality theory of spin-glass transitions, and are receiving support from the recent experiments. In particular, the detection of the chiral order using a Hall probe might open up a new area in condensed-matter physics. We also found several novel ordering properties in the issue of, (iv) magnetic ordering of Heisenberg antiferromagnets on a pyrochlore lattice.