Magnetic ordering of weakly coupled frustrated quantum spin chains

The ordering temperature of a quasi-one-dimensional system, consisting of weakly interacting quantum spin-1/2 chains with antiferromagnetic spin-frustrating couplings (or zig-zag ladder) is calculated. The results show that a quantum critical point between two phases of the one-dimensional subsystem plays a crucial role. If the one-dimensional subsystem is in the antiferromagnetic-like phase in the ground state, similar to the phase of a spin chain without frustration, weak couplings yield magnetic ordering of the Neel type. For intra-chain spin-frustrating interactions larger than the critical one (at which the quantum phase transition takes place), the quasi-one-dimensional spin system manifests a spiral magnetic incommensurate ordering. The obtained results of our quantum theory are compared with the quasi-classical approximations. The calculated features of magnetic ordering are expected to be generic for weakly coupled quantum spin chains with gapless excitations and spin-frustrating nearest and next-nearest neighbor interactions.