  The stability of the ferromagnetic phase of the 2D quantum spin-1/2 model
with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic
interactions is studied. It turns out that values of exchange integrals at
which the ferromagnetic state becomes unstable with respect to a creation of
one and two magnon are different. This difference shows that the classical
approximation is inapplicable to the study of the transition from the
ferromagnetic to the singlet state in contrast with 1D case. This problem is
investigated using a variational function of new type. It is based on the boson
representation of spin operators which is different from the Holstein-Primakoff
approximation. This allows us to obtain the accurate estimate of the transition
point and to study the character of the phase transition.
