Weakly anisotropic frustrated zigzag spin chain

The frustrated spin-$1∕2$ model with weakly anisotropic ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchanges is studied with use of variational mean-field approach, scaling estimates of the infrared divergencies in the perturbation theory and finite-size calculations. The ground-state phase diagram of this model contains three phases: the ferromagnetic phase, the commensurate spin-fluid phase, and the incommensurate phase. The nontrivial behavior of the boundaries between these phases and the character of the phase transitions in case of weak anisotropy are determined.