Using a Monte Carlo method, we study the finite-temperature phase transition in the two-dimensional classical Heisenberg model on a triangular lattice with or without easy-plane anisotropy. The model takes account of competing interactions: a ferromagnetic nearest-neighbor interaction $J_1$ and an antiferromagnetic third nearest-neighbor interaction $J_3$. As a result, the ground state is a spiral spin configuration for $-4 < J_1/J_3 < 0$. In this structure, global spin rotation cannot compensate for the effect of 120-degree lattice rotation, in contrast to the conventional 120-degree structure of the nearest-neighbor interaction model. We find that this model exhibits a first-order phase transition with breaking of the lattice rotation symmetry at a finite temperature. The transition is characterized as a $Z_2$ vortex dissociation in the isotropic case, whereas it can be viewed as a $Z$ vortex dissociation in the anisotropic case. Remarkably, the latter is continuously connected to the former as the magnitude of anisotropy decreases, in contrast to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. \textbf{79} (2010) 073001.] in which both the transitions were found to be continuous.
Interplay of anisotropy and frustration: triple transitions in a triangular-lattice antiferromagnet
本文研究了三角晶格上单离子易轴各向异性的经典海森堡反铁磁体。构造了外磁场中的平均场相图。通过零场蒙特卡罗模拟，发现了三个有限温度Berezinskiii-Kosterlitz-无相变。两个上部的过渡与离散的${\mathbb Z}_{6}$对称群的破缺有关，而最低的过渡与横向分量的准长程有序有关。第一和第二转变之间的中间共线相位是由J. V. José { \it et al}预测的滑动相位。[Phys. Rev. B { \bf 16}，1217（1977）]。
Skyrmion crystal in the RKKY system on the two-dimensional triangular lattice
我们通过广泛的蒙特卡罗模拟研究了二维三角晶格上各向同性RKKY海森堡模型的有序性质，以深入了解金属磁体的手征简并斯基米子晶体（SkX）。我们的哈密顿量只包含来自球形费米面的自旋二次RKKY相互作用，不包含嵌套和多体相互作用。SkX相是稳定的应用领域的挫折与振荡性质的RKKY相互作用和涌现的多体相互作用所产生的热波动发挥重要作用。在我们最近对3D RKKY模型的研究[Phys. Rev. B 104，184432（2021）]中报告的复本对称性破缺在当前的2D模型中不存在。SkX的形成机制的影响进行了讨论。
