Persistence in systems with algebraic interaction

Abstract

Persistence in coarsening 1D spin systems with a power law interaction $r^{-1-\sigma }$ is considered. Numerical studies indicate that for sufficiently large values of the interaction exponent $\sigma$ ($\sigma \ge 1/2$ in our simulations), persistence decays as an algebraic function of the length scale $L$, $P(L)\sim L^{-\theta }$. The Persistence exponent $\theta$ is found to be independent on the force exponent $\sigma$ and close to its value for the extremal ($\sigma \to \infty$) model, $\bar{\theta }=\mathrm{0.17507588...}$. For smaller values of the force exponent ($\sigma <1/2$), finite size effects prevent the system from reaching the asymptotic regime. Scaling arguments suggest that in order to avoid significant boundary effects for small $\sigma$, the system size should grow as ${[\mathcal{O}(1/\sigma )]}^{1/\sigma }$.

4 pages 4 figures

References in corpus (1)

• Persistence, Poisoning, and Autocorrelations in Dilute Coarsening

Cited by in corpus (3)

• Phase ordering kinetics of the long-range Ising model
• Local Persistence in the Directed Percolation Universality Class
• Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model