Existence of Antiferromagnetism and a Singlet State in the Three-Dimensional Quantum Heisenberg Model with a Random Spatially Anisotropic Distribution of Exchange Interactions with S = 1/2

摘要

The quantum Monte Carlo method was used to study antiferromagnets (AF) with a spatially Anisotropic (#lambda# = J_2 / J_1 1) Gaussian distribution of between nearest neighbors and with a random alternating exchange (I/J_1 = 1 +- #delta#) in the approximation of the self-consistent sublattice field for spin S = 1/2. The phase boundary of the domain of stability of antiferromagnetism (AFM) D_c = 1.2(2) z #lambda# (where z is the number of nearest-neighbor chains) is calculated on the "exchange dispersion (D)-normalized interchain interaction (#lambda# = J_2/J_1)" plane. Approximate dependences for the sublattice magnetization #sigma# (D) ≈ 0.80(4)(D_c - D)~(0.41(3)), energy E(D) - E(0) ≈ - #lambda# /exp (1.5z #lambda# / D), and correlation length #xi# (D) ≈ 85(4) #lambda# ln (1/(D_c - D)) for #lambda# < 0.25 were found. In the model with random alternating exchange, the region of the singlet state with a gap at D <= D_c = 0.45(7) #delta#~(0.7(1)) was determined. For the amorphous spin-Peierls compound CuGeO_3, the dispersion of exchange interactions (D~(1/2) = 72 K) was calculated.