  The one-dimensional quantum spin-1/2 model with nearest-neighbor
ferromagnetic and next-nearest-neighbor antiferromagnetic interaction is
considered. The Hamiltonian is first bosonized by using the linear spin wave
approximation, and then is treated by using the Green's function approach. An
integral expression of the quantum correction to the classical ground state
energy is derived. The critical behavior of the ground state energy in the
vicinity of the transition point from the ferromagnetic to the singlet ground
state is analyzed by numerical calculation, and the result is $-8\gamma^2$.
