  We discuss low-temperature properties of magnets with integer spin and large
single-ion easy-plane anisotropy $D$ in transverse magnetic field $h$.
Considering the exchange interaction between spins as a perturbation and using
the diagram technique we derive at $h\sim D$ in the first nonvanishing orders
of the perturbation theory thermal corrections to the elementary excitation
spectrum, magnetization and specific heat. An expression for the boundary
$h_{c1}(T)$ is found in the $h$-$T$ plane between the paramagnetic phase and
that with the long range magnetic order. The effective interaction is derived
between bosons near the quantum critical point $h_{c1}(0)$. The proposed theory
describes well experimental data obtained in $\rm NiCl_2$-$\rm 4SC(NH_2)_2$
(DTN).
