Langer's nucleation rate reproduced on the lattice

TL;DR

This paper demonstrates that Langer's bubble nucleation rate aligns quantitatively with lattice simulations, marking a significant advancement in understanding metastable phase decay and resolving previous discrepancies.

Contribution

The authors translate Langer's perturbative nucleation rate into a nonperturbative lattice-compatible form, achieving quantitative agreement and measuring higher-order contributions.

Findings

Langer's rate matches lattice results within small corrections.

Failure to fully thermalize explains previous discrepancies.

Measured two-loop coefficient on the lattice.

Abstract

We show that Langer's rate of bubble nucleation is quantitatively correct up to small higher-loop corrections, in comparison to lattice simulations. These results are a significant advancement on decades of lattice studies showing only qualitative trends, and the first showing agreement for any conservative system. We confirm that the failure to fully thermalize the metastable phase explains discrepancies with recent lattice studies that found disagreement with Langer's rate. The key theoretical development is the translation of Langer's perturbative definition of a thermal metastable phase into a nonperturbative statement that can be implemented on the lattice. Our statistical and systematic errors are small enough to allow us to measure on the lattice the coefficient of the two-loop contribution, missing from the perturbative prediction. Our conclusions also exclude a possible systematic uncertainty in $^3$He experiments.