Three-dimensional ordering in weakly coupled antiferromagnetic ladders and chains

A theoretical description is presented for low-temperature magnetic-field-induced three-dimensional (3D) ordering transitions in strongly anisotropic quantum antiferromagnets, consisting of weakly coupled antiferromagnetic spin-1/2 chains and ladders. First, effective continuum field theories are derived for the one-dimensional subsystems. Then the Luttinger parameters, which determine the low-temperature susceptibilities of the chains and ladders, are calculated from the Bethe ansatz solution for these effective models. The 3D ordering transition Line is obtained using a random-phase approximation for the weak interchain (interladder) coupling. Finally, considering a Ginzburg criterion, the fluctuation corrections to this approach are shown to be small. The nature of the 3D ordered phase resembles a Bose condensate of integer-spin magnons. It is proposed that for systems with higher spin degrees of freedom, e.g., N-leg spin-1/2 ladders, multicomponent condensates can occur at high magnetic fields.