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

The quantum Monte Carlo method was used to study antiferromagnets (AF) with a spatially anisotropic (lambda = J(2)/J(1) << 1) Gaussian distribution of bonds 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 an tiferromagnetism (AFM) D-c = 1.2(2)z lambda (where z is the number of neare st-neighbor chains) is calculated on the "exchange dispersion (D)-normalize d interchain interaction (lambda = J(2)/J(1))" plane. Approximate dependenc es for the sublattice magnetization sigma (D) approximate to 0.80(4)(D-c - D)(0.41(3)), energy E(D)- E(0) approximate to -lambda /exp(1.5z lambda /D), and correlation length xi (D) approximate to 85(4)lambda ln(1/(D-c - D)) f or lambda < 0.25 were found. In the model with random alternating exchange, the region of the singlet state with a gap at D <less than or equal to> D- c = 0.45(7)delta (0.7(1)) was determined. For the amorphous spin-Peierls co mpound CuGeO3, the dispersion of exchange interactions(rootD = 72 K) was ca lculated.