  We report the calculation of cavity exciton-polariton phase diagram which
takes into account the presence of realistic structural disorder. Polaritons
are modelled as weakly interacting two-dimensional bosons. We show that with
increasing density polaritons first undergo a quasi-phase transition towards a
Bose glass: the condensate is localized in at least one minimum of the disorder
potential, depending on the value of the chemical potential of the polariton
system. A further increase of the density leads to a percolation process of the
polariton fluid which gives rise to a Kosterlitz-Thouless phase transition
towards superfluidity. The spatial representation of the condensate
wavefunction as well as the spectrum of elementary excitations are obtained
from the solution of the Gross-Pitaevskii equation for all the phases.
