Statistical approaches to the problem of homogeneous melting of solids in the microcanonical ensemble

Melting is a common phenomenon in our daily life, and although it is understood in thermodynamic (macroscopic) terms, the transition itself has eluded a description from the point of view of microscopic dynamics. While there are studies of metastable states in classical spin Hamiltonians, cellular automata, glassy systems and other models, the statistical mechanical description of the microcanonical superheated solid state is lacking.

Our work is oriented to the study of the melting process of superheated solids, which is believed to be caused by thermal vacancies in the crystal or by the occupation of interstitial sites. When the crystal reaches a critical temperature, it becomes unstable and a collective self-diffusion process is triggered. These studies are often observed in a microcanonical environment, revealing long-range correlations due to collective effects, and from theoretical models using random walks over periodic lattices. Our results suggest that the cooperative motion made possible by the presence of vacancy-interstitial pairs (Frenkel pairs) above the melting temperature can induce long-range effective interatomic forces even beyond the neighboring fourth layer. From microcanonical simulations it is also known that an ideal crystal needs a random waiting time until the solid phase collapses. Regarding this, our results also point towards a description of these waiting times using a statistical model in which there is a positive quantity X that accumulates from zero in incremental steps, until it exceeds a threshold value.