  For theoretical description of pseudospin systems with essential short-range
and long-range interactions we use the method based on calculations of the free
energy functional with taking into account the short-range interactions within
the reference approach in cluster approximation. We propose a consistent
formulation of the cluster expansion method for quantum pseudospin systems. We
develop a method allowing one to obtain within the cluster approximation an
Ornstein-Zernike type equation for reference cumulant Green function of an
arbitrary order. In the two-particle cluster approximation we derived an
explicit expression for pair temperature cumulant Green function of the
reference system. In the cluster random phase approximation we calculated and
studied thermodynamic characteristics, elementary excitation spectrum, and
integral intensities of the Ising model in transverse field.
