Flow-based Nonperturbative Simulation of First-order Phase Transitions

TL;DR

This paper introduces a flow-based sampling method to efficiently simulate first-order phase transitions and calculate nucleation rates in lattice scalar field theories, addressing mode-collapse and rare-event challenges.

Contribution

The paper proposes the partitioning flow-based MCMC method, a novel approach that improves sampling of hierarchical distributions and rare events in lattice field theory simulations.

Findings

Successfully models hierarchical order parameter distributions

Effectively simulates critical bubble configurations

Facilitates nucleation rate calculations

Abstract

We present a flow-based method for simulating and calculating nucleation rates of first-order phase transitions in scalar field theory on a lattice. Motivated by recent advancements in machine learning tools, particularly normalizing flows for lattice field theory, we propose the ``partitioning flow-based Markov chain Monte Carlo (PFMCMC) sampling" method to address two challenges encountered in normalizing flow applications for lattice field theory: the ``mode-collapse" and ``rare-event sampling" problems. Using a (2+1)-dimensional real scalar model as an example, we demonstrate the effectiveness of our PFMCMC method in modeling highly hierarchical order parameter probability distributions and simulating critical bubble configurations. These simulations are then used to facilitate the calculation of nucleation rates. We anticipate the application of this method to (3+1)-dimensional theories for studying realistic cosmological phase transitions.