Abstract We consider a two dimensional compass model with a next and a next near Heisenberg term. The interactions are of two types: frustrated near neighbor compass interactions of amplitudes J x and J y , and next and next near neighbor Heisenberg interactions with exchanges J 1 and J 2 respectively. The Heisenberg interactions are isotropic in spin space, but the compass interactions depend on the bond direction. The ground state of the pure compass model is degenerated with a complex phase diagram. This degeneracy is removed by the Heisenberg terms leading to the arising of a magnetically ordered phase with a preferred direction. We calculate the phase diagrams at zero temperature for the case where, for J 2 = 0, we have an antiferromagnetic ground state. We show that varying the value of J 2 , a magnetically disordered phase can be reached for small values of the compass interactions. We also calculate the critical temperature for a specified value of parameters.

中文翻译：

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具有海森堡相互作用的二维罗盘模型

摘要 我们考虑一个具有下一个和下一个近海森堡项的二维罗盘模型。相互作用有两种类型：振幅为 J x 和 J y 的受挫近邻罗盘相互作用，以及分别与交换 J 1 和 J 2 的下一个和下一个近邻海森堡相互作用。海森堡相互作用在自旋空间中是各向同性的，但罗盘相互作用取决于键的方向。纯罗盘模型的基态用复杂的相图退化。海森堡项消除了这种简并性，导致出现具有优选方向的磁性有序相。我们计算零温度下的相图，其中 J 2 = 0，我们有一个反铁磁基态。我们表明，改变 J 2 的值，对于较小的罗盘相互作用值，可以达到磁无序相。我们还计算指定参数值的临界温度。