Dimer state in the two-dimensional anisotropic alternated-exchange Heisenberg model

An analysis is made of the two-dimensional Heisenberg model with S=1/2, anisotropic exchange interaction between nearest neighbors, and alternating exchange in two directions, [100] and [010] (corresponding to condensation of the (π, π) mode) and in one direction [100] (corresponding to condensation of the (π, 0) mode). The quantum Monte Carlo method is used to calculate the thermodynamic characteristics and the spin correlation functions which are used as the basis to determine the boundary of stability of an anisotropic antiferromagnetic with respect to alternation of exchange δ=(1−Jx,y/Jz)0.4 in the (π,π) model and δ=(1−Jx,y/Jz)0.31 in the (π,0) model. In the (π,0) model a disordered quantum state exists in the range (1−Jx,y/Jz)0.31<δ<(0.3–0.35). The energy (E−0.68)=0.36δ1.80(6) and 0.21 δ2.0(5), the energy gap between the ground and excited states Hc(δ)=1.96δ2.(1), 1.8(1) (δ−0.35(3))0.67(2) were determined as a function of the alternation of exchange in the (π,π)-and (π,0) models, respectively.