Scaling Monte Carlo kinetics of the Potts model using rate theory

Abstract A method is introduced for scaling Monte Carlo kinetics of the Potts model using rate theory. The method is particularly designed for the kinetic and spatial scaling of multistate kinetic Potts models using one or more sets of non-conserved structural or orientational state variables S i each of which can assume a number of Q i degenerate ground states ( Q or multistate Potts models) as commonly employed for simulating recrystallization and curvature driven grain growth phenomena. The approach is based on the equivalence of single-site state switches in the Potts model and grain boundary motion as described by Turnbull's classical rate theory mapped on a simulation lattice. According to this approach the switching probabilities can be scaled by the ratio of the local and the maximum occurring values of the grain boundary mobility and by the ratio of the local and the maximum occurring values of configurational and scalar contributions to the driving force. The real time step elapsing during one Monte Carlo time step is scaled by the maximum occurring grain boundary mobility, the maximum occurring driving force, and the lattice parameter of the simulation grid.