Frustrated ferromagnetic spin-1/2 chain in the magnetic field

We study the ground state properties of the Heisenberg spin-1/2 chain with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions using two approximate methods. One of them is the Jordan-Wigner mean-field theory and another approach based on the transformation of spin operators to bose-ones and on the variational treatment of bosonic Hamiltonian. Both approaches give close results for the ground state energy and the T=0 magnetization curve. It is shown that quantum fluctuations change the classical critical exponents in the vicinity of the transition point from the ferromagnetic to the singlet ground state. The magnetization process displays the different behavior in the regions near and far from the transition point. The relation of the obtained results to experimental magnetization curve in $Rb_{2}Cu_{2}Mo_{3}O_{12}$ is discussed.