论文标题
四维柏拉图固体的经典磁化
Classical magnetization of a four-dimensional Platonic solid
论文作者
论文摘要
600细胞是一种常规的4个聚体，是柏拉图固体的四维类似物。三维柏拉图固体具有二维的柏拉图固体，当显示在经典和量子水平的外部场中，在其顶部上安装在其顶点上的旋转相互作用时，在外部场上具有不连续的地面磁化响应。不连续性不是由于自旋空间中的各向异性，而是由于分子的特殊连通性。在这里，对于安装在600细胞的120个顶点上的经典旋转，考虑了磁场中最近的邻居抗铁磁XX和Heisenberg模型。地面磁化响应富含，其特征是XX情况下六个磁化不连续性，在海森伯格案中，六个磁化强度和三个易感性不合时宜。这表明从三个到四个空间维度富含地下磁化响应。
The 600-cell is a regular 4-polytope that is a four-dimensional analog of a Platonic solid. Three-dimensional Platonic solids with icosahedral $I_h$-symmetry have been shown to have a discontinuous ground-state magnetization response in an external field at the classical and quantum level, when spins mounted on their vertices interact according to the antiferromagnetic Heisenberg model. The discontinuities are not due to anisotropy in spin space, but rather to the special connectivity of the molecules. Here the nearest-neighbor antiferromagnetic XX and Heisenberg models in a magnetic field are considered for classical spins mounted on the 120 vertices of the 600-cell. The ground-state magnetization response is rich, characterized by six magnetization discontinuities in the XX case, and six magnetization and three susceptibility discontinuities in the Heisenberg case. This demonstrates that going from three to four spatial dimensions enriches the ground-state magnetization response.
