Barrier crossing in a two-state system: Effect of bias and stochastic fields

We study barrier crossing in a two-state system, namely the kinetic Ising model, in the presence of a weak bias field and spatially homogeneous, but time-dependent, Gaussian random fields. We find that the bias field determines the location of the dominant maxima of the probability distribution function of the magnetization, whereas the noise intensity controls their sharpness and stability of the distribution. A moderate stochastic field lowers the effective energy barrier and facilitates transitions between ordered states, while strong noise induces broad distributions and significant backflow, which reduces directional selectivity. Our results suggest that efficient barrier crossing requires a balanced combination of moderate stochastic driving and controlled bias.