A nonperturbative test of nucleation calculations for strong phase transitions

TL;DR

The paper tests the reliability of nucleation-rate calculations for first-order phase transitions in thermal field theory by performing nonperturbative lattice simulations of a real scalar 3d EFT with a tree-level barrier and comparing the nucleation rate $\Gamma$ to perturbative predictions (tree-level, LPA, and full one-loop). The main result is that the lattice yields a precise nonperturbative value for $|\log \Gamma|$ that differs from the full one-loop estimate by about 20%, while the tree-level and LPA approximations are notably less accurate for the rate. This nonperturbative benchmark challenges some assumptions of the current nucleation paradigm and motivates a two-loop calculation for a definitive test. The work provides a robust reference for cosmological phase-transition studies and gravitational-wave predictions and highlights the need for faster sampling methods to enable broader phenomenological use.

Abstract

Nucleation rate computations are of broad importance in particle physics and cosmology. Perturbative calculations are often used to compute the nucleation rate $Γ$, but these are incomplete. We perform nonperturbative lattice simulations of nucleation in a scalar field theory with a tree-level barrier, computing a final result extrapolated to the thermodynamic and continuum limits. Although the system in question should be well-described by a complete one-loop perturbative calculation, we find only qualitative agreement with the full perturbative result, with a 20% discrepancy in $|\log Γ|$. Our result motivates further testing of the current nucleation paradigm.

Figures (4)

• Figure 1: Probability distribution $P(\theta_\text{op})$ of the order parameter at some temperature below $T_\mathrm{c}$. The metastable and stable phases are separated by an exponentially suppressed area, the mixed critical bubble. The separatrix configurations are drawn from the narrow range $\epsilon$ around the critical bubble.
• Figure 2: Snapshots of a nucleating bubble with lattice size $L\lambda_3 = 72$ and spacing $a\lambda_3=1.5$. We remove ultraviolet fluctuations by performing eight steps of nearest neighbour averaging. Here, $t=0\Delta t$ corresponds to the initial separatrix configuration and the negative time direction describes the backward time evolution. Note that the snapshots are not evenly spaced in time.
• Figure 3: The zero lattice spacing (top) and infinite volume (bottom) extrapolations, together with cubic, cubic plus quartic and exponential fits respectively. The vertical line in the top plot marks a perturbative estimate of the correlation length.
• Figure 4: The nucleation rate as a function of temperature. Uncertainty bands for the tree-level and one-loop perturbative results are based on varying the renormalisation scale over $\mu_3/\lambda_3 \in \{0.5, 1, 2\}$. The uncertainty estimate on the LPA relflects different choices for removing imaginary parts of the potential. The lattice points are continuum extrapolated; the red triangle highlights the temperature actually simulated, while the orange circles have utilised reweighting. The orange continuous line is the reweighted result for $a\lambda_3=1.5$, $L\lambda_3=60$. The results in this figure are tabulated at gould_2024_11085693.