  The temperature and chemical potential dependent surface tension of bags is
introduced into the gas of quark-gluon bags model. This resolves a long
standing problem of a unified description of the first and second order phase
transition with the cross-over. Such an approach is necessary to model the
complicated properties of quark-gluon plasma and hadronic matter from the first
principles of statistical mechanics. The suggested model has an exact
analytical solution and allows one to rigorously study the vicinity of the
critical endpoint of the deconfinement phase transition. The existence of
higher order phase transitions at the critical endpoint is discussed. In
addition, we found that at the curve of a zero surface tension coefficient
there must exist the surface induced phase tranition of the 2$^{nd}$ or higher
order, which separates the pure quark gluon plasma (QGP) from the cross-over
states, that are the mixed states of hadrons and QGP bags. Thus, the present
model predicts that the critical endpoint of quantum chromodynamics is the
tricritical endpoint.
