Parametric links among Monte Carlo, phase-field, and sharp-interface models of interfacial motion

Parametric links are made among three mesoscale simulation paradigms: phase-field, sharp-interface, and Monte Carlo. A two-dimensional, square lattice, 1/2 Ising model is considered for the Monte Carlo method, where an exact solution for the interfacial free energy is known. The Monte Carlo mobility is calibrated as a function of temperature using Glauber kinetics. A standard asymptotic analysis relates the phase-field and sharp-interface parameters, and this allows the phase-field and Monte Carlo parameters to be linked. The result is derived without bulk effects but is then applied to a set of simulations with the bulk driving force included. An error analysis identifies the domain over which the parametric relationships are accurate.