The investigation of the critical phenomena of the competing spin systems with the higher order spin interaction on the bulk and thin film

ANNNI和A3 NNI模型是我们所熟悉的自旋系统，具有不同范围（例如，第一，第二和第三最近邻）的相互作用之间的竞争。在本研究中，我们考虑了具有高阶自旋相互作用的S=1 ANNNI和A3 NNI模型。利用解析方法和Monte Carlo模拟，我们研究了高阶自旋相互作用和自旋量子数在竞争自旋系统中的作用和重要性，1）扩展的A_3NNI模型我们提出了以高阶自旋相互作用为模型的扩展的A_3NNI模型，解释了UNi_2Si_2中从k=1/3调制结构到反铁磁结构的相变. 2）薄膜上的扩展ANNNI模型用MC方法计算了S=1的ANNNI模型在3位4自旋相互作用下的磁相图，有限尺寸标度表明4条相变线为二级相变。这些结果表明了四临界点的存在。3）具有交替层间相互作用的扩展ANNNI模型利用MC非平衡弛豫方法和有限尺寸标度，计算了临界温度和临界指数。所得到的指数表明，普通的普遍性不成立，并建议弱普遍性成立。

The ANNNI and A3NNI models are familiar as the spin systems with the competition between interactions with different range (for example, 1st, 2nd, and 3rd nearest-neighbors). In this study, we consider the S=1 ANNNI and A3NNI models with the higher order spin interaction. Using the analytical methods and the Monte Carlo simulation (MC), we investigate the role and importance of the higher order spin interaction and the spin quantum number in the competing spin systems, theoretically.1) The extended A3NNI modelWe propose the extended A3NNI model with the higher order spin interaction as model explaining the phase transition from the k=1/3 modulated structure to the antiferromagnetic structure in UNi2Si2. The temperature dependence of the Fourier coefficients in the Modulated structures are calculated by MC, and we show the appearance of this phase transition.2) The extended ANNNI model on the thin filmUsing MC, the magnetic phase diagram of S=1 ANNNI model with the 3-site 4-spin interaction is obtained, and the finite-size scaling shows that 4 phase transition lines are the second order phase transition. These results suggest the existence of the tetracritical point.3) The extended ANNNI model with alternating intralayer interactionsUsing MC with non-equilibrium relaxation method and the finite-size scaling, we calculated critical temperatures and critical exponents. The obtained exponents show that the ordinary universality does not hold in this model, and suggests that the weak universality holds.