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

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.