  The effect of subcritical hadron bubbles on a first-order quark-hadron phase
transition is studied. These subcritical hadron bubbles are created due to
thermal fluctuations, and can introduce a finite amount of phase mixing (quark
phase mixed with hadron phase) even at and above the critical temperature. For
reasonable choices of surface tension and correlation length, as obtained from
the lattice QCD calculations, we show that the amount of phase mixing at the
critical temperature remains below the percolation threshold. Thus, as the
system cools below the critical temperature, the transition proceeds through
the nucleation of critical-size hadron bubbles from a metastable quark-gluon
phase (QGP), within an inhomogeneous background populated by an equilibrium
distribution of subcritical hadron bubbles. The inhomogeneity of the medium
results in a substantial reduction of the nucleation barrier for critical
bubbles. Using the corrected nucleation barrier, we estimate the amount of
supercooling for different parameters controlling the phase transition, and
briefly discuss its implications to cosmology and heavy-ion collisions.
