We study a frustrated two-leg spin ladder with alternate isotropic Heisenberg and Ising rung exchange interactions, whereas, interactions along legs and diagonals are Ising-type. All the interactions in the ladder are anti-ferromagnetic in nature and induce frustration in the system. This model shows four interesting quantum phases: (i) stripe rung ferromagnetic (SRFM), (ii) stripe rung ferromagnetic with edge singlet (SRFM-E), (iii) anisotropic antiferromagnetic (AAFM), and (iv) stripe leg ferromagnetic (SLFM) phase. We construct a quantum phase diagram for this model and show that in stripe rung ferromagnet (SRFM), the same type of sublattice spins (either isotropic S-type or discrete anisotropic σ-type spins) are aligned in the same direction. Whereas, in anisotropic antiferromagnetic phase, both S and σ-type of spins are anti-ferromagnetically aligned with each other, two nearest S spins along the rung form an anisotropic singlet bond whereas two nearest σ spins form an Ising bond. In large Heisenberg rung exchange interaction limit, spins on each leg are ferromagnetically aligned, but spins on different legs are anti-ferromagnetically aligned. The thermodynamic quantities like specific heat C _v (T), magnetic susceptibility χ(T) and thermal entropy S(T) are also calculated using the transfer matrix method for various phases. The magnetic gap in the SRFM and the SLFM can be noticed from χ(T) and C _v (T) curves.

我们研究了具有交替各向同性海森堡和伊辛梯级交换相互作用的受挫双腿自旋梯，而沿腿和对角线的相互作用是伊辛型的。梯子中的所有相互作用本质上都是反铁磁的，会导致系统受挫。该模型显示了四个有趣的量子相：(i) 条形铁磁 (SRFM)，(ii) 带边缘单线态的条形铁磁 (SRFM-E)，(iii) 各向异性反铁磁 (AAFM)，以及 (iv) 条形铁磁（ SLFM) 阶段。我们为该模型构建了一个量子相图，并表明在条形铁磁体 (SRFM) 中，相同类型的亚晶格自旋（各向同性S型或离散各向异性σ型自旋）在同一方向上对齐。而在各向异性反铁磁相中，S型和σ型自旋彼此反铁磁排列，沿梯级的两个最近的S自旋形成各向异性单重键，而两个最近的σ自旋形成 Ising 键。在大的海森堡梯级交换相互作用极限中，每条腿上的自旋是铁磁对齐的，但不同腿上的自旋是反铁磁对齐的。比热C _v ( T )、磁化率χ ( T ) 和热熵S ( T ) 等热力学量 ) 也使用传递矩阵法计算各种相。从χ ( T ) 和C _v ( T ) 曲线可以看出 SRFM 和 SLFM 中的磁隙。