The order, shape and critical point for the phase transition between the
hadronic matter and quark-gluon plasma are considered in a thermodynamical
consistent approach. The hadronic phase is taken as Van der Waals gas of all
the known hadronic mass spectrum particles mH≤2.0 GeV as well as Hagedorn
bubbles which correspond hadronic states with mass spectrum mH>2.0 GeV. The
density of states for Hagedorn bubbles is derived by calculating the
microcanonical ensemble for a bag of quarks and gluons with specific internal
color-flavor symmetry. The mixed-grand and microcanonical ensembles are derived
for massless and massive flavors. We find Hagedorn bubbles are strongly
suppressed in the dilute hadronic matter and they appear just below the line of
the phase transition. The order of the phase transition depends on Hagedorn
bubble's internal color-flavor structure and the volume fluctuation as well. On
the other hand, the highly compressed hadronic matter undergoes a smooth phase
transition from the gas of known mass spectrum hadrons to another one dominated
by Hagedorn bubbles with specific internal color-flavor structure before the
phase transition to quark-gluon plasma takes place at last. The phase
transition is found a first order for the intermediate and large chemical
potentials. The existence of the tri-critical point depends on the modification
of the bubble's internal structure specified by a phenomenological parameter
γ∝μB in the medium.Comment: 69 pages, 10 figure