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Persistence in higher dimensions : a finite size scaling study

G. Manoj·P. Ray
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Abstract

We show that the persistence probability $P(t,L)$, in a coarsening system of linear size $L$ at a time $t$, has the finite size scaling form $P(t,L)\sim L^{-zθ}f(\frac{t}{L^{z}})$ where $θ$ is the persistence exponent and $z$ is the coarsening exponent. The scaling function $f(x)\sim x^{-θ}$ for $x \ll 1$ and is constant for large $x$. The scaling form implies a fractal distribution of persistent sites with power-law spatial correlations. We study the scaling numerically for Glauber-Ising model at dimension $d = 1$ to 4 and extend the study to the diffusion problem. Our finite size scaling ansatz is satisfied in all these cases providing a good estimate of the exponent $θ$.

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G. Manoj, P. Ray. 2000-09-13. Persistence in higher dimensions : a finite size scaling study. https://doi.org/10.1103/physreve.62.7755

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