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Global evolution of the matter in relativistic collisions of heavy nuclei andthe resulting global freeze-out parameters are analyzed in a wide range ofincident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis isperformed within the three-fluid model employing three different equations ofstate (EoS): a purely hadronic EoS, an EoS with the first-order phasetransition and that with a smooth crossover transition. Global freeze-outparameters deduced from experimental data within the statistical model are wellreproduced within the crossover scenario. The 1st-order-transition scenario isslightly less successful. The worst reproduction is found within the purelyhadronic scenario. These findings make a link between the EoS and results ofthe statistical model, and indicate that deconfinement onset occurs at$\sqrt{s_{NN}}\gsim$ 5 GeV.

Phase Evolution and Freeze-out within Alternative Scenarios of Relativistic Heavy-Ion Collisions