论文标题
沮丧的自旋系统的一个和二维的变化分析：手性转变和磁各向异性转变
Variational analysis in one and two dimensions of a frustrated spin system: chirality transitions and magnetic anisotropic transitions
论文作者
论文摘要
我们研究了铁磁/抗铁磁挫败的自旋系统的能量，其值在一个维度和二维域中的三维单位球体的两个差异圆周。它由一个术语的总和组成，该术语取决于最接近和最新的相互作用以及计算旋转磁各向异性转变的惩罚项。我们将能量的渐近行为分析，即系统接近Helimagnet/Ferromagnet跃迁点，因为颗粒数量分歧。在一维环境中，我们计算了$γ$ - 首先和二阶能量重新归功的限制。结果，它显示了系统用于任何磁性磁管过渡和手性转变的能量。在二维环境中，通过计算二阶能量重新归一化的$γ$限制，我们证明了手学转变的几何刚度的出现和研究。
We study the energy of a ferromagnetic/antiferromagnetic frustrated spin system with values on two disjoint circumferences of the 3-dimensional unit sphere in a one-dimensional and two-dimensional domain. It consists on the sum of a term that depends on the nearest and next-to-nearest interactions and a penalizing term that counts the spin's magnetic anisotropy transitions. We analyze the asymptotic behaviour of the energy, that is when the system is close to the helimagnet/ferromagnet transition point as the number of particles diverges. In the one-dimensional setting we compute the $Γ$-limit of renormalizations of the energy at first and second order. As a result, it is shown how much energy the system spends for any magnetic anistropy transition and chirality transition. In the two-dimensional setting, by computing the $Γ$-limit of the renormalization of the energy at second order, we we prove the emergence and study the geometric rigidity of chirality transitions.
