Interplay of fast and slow dynamics in rare transition pathways: the disk-to-slab transition in the 2d Ising model

摘要

Rare transitions between long-lived stable states are often analyzed in termsof free energy landscapes computed as functions of a few collective variables.Here, using transitions between geometric phases as example, we demonstratethat the effective dynamics of a system along these variables are an essentialingredient in the description of rare events and that the static perspectiveprovided by the free energy alone may be misleading. In particular, weinvestigate the disk-to-slab transition in the two-dimensional Ising modelstarting with a calculation of a two-dimensional free energy landscape and thedistribution of committor probabilities. While at first sight it appears thatthe committor is incompatible with the free energy, they can be reconciled witheach other using a two-dimensional Smoluchowski equation that combines the freeenergy landscape with state dependent diffusion coefficients. These resultsillustrate that dynamical information is not only required to calculate rateconstants but that neglecting dynamics may also lead to an inaccurateunderstanding of the mechanism of a given process.