Reconstruction of the Free Energy in the Metastable Region using the Path Ensemble

TL;DR

This paper reconstructs the free energy landscape in the metastable region of the 3D Ising model by analyzing magnetization paths, revealing that the free energy barrier remains finite contrary to mean-field predictions.

Contribution

It introduces a method to reconstruct free energy from path ensembles in the Ising model, providing new insights into metastable transitions.

Findings

Free energy barrier remains finite in the metastable region.

Reconstructed free energy depends on magnetic field, temperature, and system size.

Contradicts mean-field theory predictions of zero barrier at transition.

Abstract

By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent distributions from which we reconstruct the free energy as a function of the magnetic field, temperature and system size. From the reconstructed free energy, we obtain the free energy barrier that is associated with the transition from a metastable state to the stable equilibrium state. Although mean-field theory predicts a sharp transition between the metastable and the unstable region where the free energy barrier is zero, the results for the nearest-neighbour Ising model show that the free energy barrier does not go zero.