Persistence in the Zero-Temperature Dynamics of the Random Ising Ferromagnet on a Voronoi-Delaunay lattice

Details Persistence in the Zero-Temperature Dynamics of the Random Ising Ferromagnet on a Voronoi-Delaunay lattice Persistence in the Zero-Temperature Dynamics of the Random Ising Ferromagnet on a Voronoi-Delaunay lattice

2002-11-05

arxiv.org/abs/cond-mat/0211097v1

Physics

Condensed Matter

Statistical Mechanics

3 pages, 3 Figures

Scientific paper

The zero-temperature Glauber dynamic is used to investigate the persistence probability $P(t)$ in the randomic 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 $J(r) \propto e^{-\alpha r}$, with $\alpha \ge 0$. The persistence probability of spins flip, that does not depends on time $t$, is found to decay to a non-zero value $P(\infty)$ depending on the parameter $\alpha$. Nevertheless, the quantity $p(t)=P(t)-P(\infty)$ 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 $\alpha$. Our results are consistent with the ones obtained for the diluted ferromagnetic Ising model on a square lattice.

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