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We investigate the process of phase conversion in a thermally-driven {\itweakly} first-order quark-hadron transition. This scenario is physicallyappealing even if the nature of this transition in equilibrium proves to be asmooth crossover for vanishing baryonic chemical potential. We construct aneffective potential by combining the equation of state obtained within LatticeQCD for the partonic sector with that of a gas of resonances in the hadronicphase, and present numerical results on bubble profiles, nucleation rates andtime evolution, including the effects from reheating on the dynamics fordifferent expansion scenarios. Our findings confirm the standard picture of acosmological first-order transition, in which the process of phase conversionis entirely dominated by nucleation, also in the case of a weakly first-ordertransition. On the other hand, we show that, even for expansion rates muchlower than those expected in high-energy heavy ion collisions, nucleation isvery unlikely, indicating that the main mechanism of phase conversion isspinodal decomposition. Our results are compared to those obtained for astrongly first-order transition, as the one provided by the MIT bag model.

Phase conversion in a weakly first-order quark-hadron transition