Effect of the Haldane gap on quasi-one-dimensional systems

A quasi-one-dimensional S=1 Heisenberg antiferromagnet with a single-ion anisotropy Dtsumⱼ(Sⱼᶻ{)}²$ is investigated. By treatment of interchain interactions with coupling constant J as a mean field, this system has been revealed to have a disordered ground state due to an effect of the Haldane gap, if J is small enough. By use of this approximation and application of the finite-size-scaling technique to a chain, the ground-state phase diagram in the JD plane is presented. This analysis leads to the prediction that Ni(C₂{H}₈N₂{)}₂NO₂(ClO₄) has no N\'eel order even at T=0. In addition it is found that the phase transition with respect to D (0) for a chain belongs to the two-dimensional Ising-model universality class, which agrees with Haldane's conjecture.