  We propose a new formulation of the statistical multifragmentation model
based on the analysis of the virial expansion for a system of the nuclear
fragments of all sizes. The developed model not only enables us to account for
short-range repulsion, but also to calculate the surface free energy which is
induced by the interaction between the fragments.
  We propose a new parameterization for the liquid phase pressure which allows
us to introduce a compressible nuclear liquid into the statistical
multifragmentation model. The resulting model is exactly solvable and has no
irregular behavior of the isotherms in the mixed phase region that is typical
for mean-field models. The general conditions for the 1-st and 2-nd (or higher)
order phase transitions are formulated. It is shown that all endpoints of the
present model phase diagram are the tricritical points, if the Fisher exponent
$\tau$ is in the range $\{3}{2} \le \tau \le 2$. The treatment of nuclear
liquid compressibility allows us to reduce the tricritical endpoint density of
the statistical multifragmentation model to one third of the normal nuclear
density. A specific attention is paid to of the fragment size distributions in
the region of a negative surface tension at supercritical temperatures.
