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

TL;DR

This study investigates how the persistence probability in a 2D random ferromagnetic Ising model on a Voronoi-Delaunay lattice behaves at zero temperature, revealing non-zero long-term persistence and exponential decay of fluctuations.

Contribution

It introduces a detailed analysis of persistence in a disordered 2D Ising model with distance-dependent couplings on a Voronoi-Delaunay lattice, extending understanding of non-equilibrium dynamics in disordered systems.

Findings

Persistence probability approaches a non-zero limit depending on disorder parameter.

The difference from the long-term persistence decays exponentially.

The fraction of unflipped spins increases with disorder parameter .

Abstract

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.