Persistence in the zero-temperature dynamics of the random Ising ferromagnet on a Voronoi–Delaunay lattice

Abstract The zero-temperature Glauber dynamic is used to investigate the persistence probability P ( t ) in the random two-dimensional ferromagnetic Ising model on a Voronoi–Delaunay tessellation. We consider the coupling factor J varying with the distance r between the first neighbors to be J ( r )∝e − αr , with α ⩾0. The persistence probability P (∞), that does not depend on time t , is found to achieve a non-zero value that depends on the parameter α . Nevertheless, the quantity p ( t )= P ( t )− P (∞) decays exponentially to zero over long times. Furthermore, the fraction of spins that do not change at a time t is a monotonically increasing function of the parameter α . Our results are consistent with those obtained for the diluted ferromagnetic Ising model on a square lattice.