A nonperturbative lattice calculation finds that perturbative bubble nucleation rates in a tree-level barrier scalar theory agree only qualitatively, with |log Γ| off by 20% at one loop and 100% at tree level.
Langer,Theory of the condensation point,Annals Phys.41(1967) 108
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Testing nucleation calculations for strong phase transitions
A nonperturbative lattice calculation finds that perturbative bubble nucleation rates in a tree-level barrier scalar theory agree only qualitatively, with |log Γ| off by 20% at one loop and 100% at tree level.