Spin kinetics formulated in discrete time is featured in the voter model, various threshold models and others of relevance in sociophysics. The definition of such a model provides a spin's flipping probability in dependence of other spin values in the interaction neighbourhood. A straight-forward numerical simulation runs a loop in which a spin is chosen uniformly at random, the flipping probability is calculated and, accordingly, the spin is flipped or not. When flipping probabilities are small, however, this direct implementation becomes inefficient, spending many idle rounds of the loop without actual flipping events. An event-driven implementation, e.g. a discrete time analogue of the Gillespie algorithm, increases efficiency by selecting a spin proportional to its flipping probability and directly skipping idle steps between flipping events. An additional challenge arises when flipping probabilities change also at non-event time steps. Prominently this is the case with age-dependent dynamics where flipping probability depends explicitly on time since the last flip. We introduce a simulation technique geared towards age-dependent dynamics and demonstrate its performance gain.
Detalles de contacto:
Juan Fernández Gracia Contact form