  The short-range correlations are considered for a two-dimensional hard-core
boson model on square lattice within Bethe approximation for the clusters
consisting of two and four sites. Explicit equations are derived for the
critical temperatures of charge and superfluid ordering and their solutions are
considered for various ratios of the charge-charge correlation parameter to the
transfer integral. It is shown that taking into account short-range
correlations for the temperatures of charge ordering results in the appearance
of the critical concentration of bosons, which restricts the existence domain
of the solutions of charge ordering type. In the case of superfluid ordering
with the assumption of short-range correlations, the critical temperature is
reduced up to zero values at half-filling. A phase diagram of the hard-core
boson model is constructed with the assumption of phase separation within
Maxwell's construction and it is shown that taking into account short-range
correlations within Bethe approximation quantitatively approximates the form of
phase diagram to the results of the quantum Monte Carlo method.
