  We present a few explicit counterexamples to the widely spread belief about
an exclusive role of the bimodal nuclear fragment size distributions as the
first order phase transition signal. In thermodynamic limit the bimodality may
appear at the supercritical temperatures due to the negative values of the
surface tension coefficient. Such a result is found within a novel exactly
solvable formulation of the simplified statistical multifragmentation model
based on the virial expansion for a system of the nuclear fragments of all
sizes. The developed statistical model corresponds to the compressible nuclear
liquid with the tricritical endpoint located at one third of the normal nuclear
density. Its exact solution for finite volumes demonstrates the bimodal
fragment size distribution right inside the finite volume analog of a gaseous
phase. These counterexamples clearly demonstrate the pitfalls of Hill approach
to phase transitions in finite systems.
