Modeling a dimer state in CuGeO3 in the two-dimensional anisotropic Heisenberg model with alternated exchange interaction

The two-dimensional Heisenberg spin-1/2 model with alternated exchange interaction along the c axis and an anisotropic distribution of the exchange interaction in the lattice, J _b/J _c=0.1, is examined. A quantum Monte Carlo method is used to calculate the phase diagrams of the antiferromagnet, the dimer state in a plane, the value of the alternation δ of the exchange interaction, and the anisotropy Δ=1−J ^xy/J ^z of the exchange interaction, Δ∼δ ^0.58(6). The following characteristics are calculated for Δ=0.25: the dependence of the temperature of the dimer-state-paramagnet transition on the alternation of the exchange interaction, T _c(δ)=0.55(4)(δ−0.082(6))^0.50(3), the singlet-triplet energy gap, and the dependence of the magnetization on the external field for some values of δ. The value of the exchange interaction, J _c=127 K, the alternation of the exchange interaction, δ=0.11J _c, and the correlation radius along the c axis, ξ _c≈28c, are determined. Finally, it is found that the temperature dependence of the susceptibility and the specific heat are in good agreement with the experimental data. Zh. éksp. Teor. Fiz. 112, 2184–2197 (December 1997)