Bayesian statistical modeling of microcanonical melting times at the superheated regime

Homogeneous melting of superheated crystals at constant energy is a dynamical process, believed to be triggered by the accumulation of thermal vacancies and their self-diffusion. From microcanonical simulations we know that if an ideal crystal is prepared at a given kinetic energy, it takes a random time t_w until the melting mechanism is actually triggered. In this work we have studied in detail the statistics of t_w for melting at different energies by performing a large number of Z-method simulations and applying state-of-the-art methods of Bayesian statistical inference. By focusing on a small system size and short-time tail of the distribution function, we show that t_w is actually gamma-distributed rather than exponential (as asserted in a previous work), with decreasing probability near t_w∼0. We also explicitly incorporate in our model the unavoidable truncation of the distribution function due to the limited total time span of a Z-method simulation. The probabilistic model presented in this work can provide some insight into the dynamical nature of the homogeneous melting process, as well as giving a well-defined practical procedure to incorporate melting times from simulation into the Z-method in order to correct the effect of short simulation times.