  The gold--gold collisions at $\sqrt{s_{NN}}=7.7$ and $11.5$GeV are simulated
within the PHSD transport model. In each collision event, the spectator
nucleons are separated and the fluidization procedure for the participants is
performed. The local velocities are determined in the Landau frame and the
kinematic and thermal vorticity fields are evaluated. We analyze the
thermodynamic properties of the cells where $\Lambda$s and
$\overline{\Lambda}$s were born or had their last interaction. Such cells
contribute to the formation of the observed global polarization of hyperons
induced by the thermal vorticity of the medium. The $\overline{\Lambda}$
polarization signal is found to be mainly determined by hot, dense, and highly
vortical cells at the earlier stage of the collision, whereas the $\Lambda$
polarization signal is accumulated over the longer time and includes cells with
lower vorticity. The calculated global polarizations for both $\Lambda$s and
$\overline{\Lambda}$s agree well with the experimental finding by the STAR
collaboration at energy $\sqrt{s_{NN}}=11.5$GeV. For collisions at
$\sqrt{s_{NN}}=7.7$GeV, we can reproduce the STAR data for $\Lambda$ hyperons,
but significantly underpredict the observed global polarization of
$\overline{\Lambda}$. Furthermore, we consider the centrality dependence of the
hyperon polarization in collisions at 7.7GeV. It increases with an increase of
centrality, reaches a maximum at 65--75%, and then starts decreasing rapidly
for peripheral collisions.
