Non-universality of aging during phase separation of the two-dimensional long-range Ising model

Abstract

We investigate the aging properties of phase-separation kinetics following quenches from $T=\infty$ to a finite temperature below $T_c$ of the paradigmatic two-dimensional conserved Ising model with power-law decaying long-range interactions $\sim r^{-(2+\sigma )}$. Physical aging with a power-law decay of the two-time autocorrelation function $C(t,t_w)\sim {\left(t/t_w\right)}^{-\lambda /z}$ is observed, displaying a complex dependence of the autocorrelation exponent $\lambda$ on $\sigma$. A value of $\lambda =3.500(26)$ for the corresponding nearest-neighbor model (which is recovered as the $\sigma \to \infty$ limes) is determined. The values of $\lambda$ in the long-range regime ($\sigma <1$) are all compatible with $\lambda \approx 4$. In between, a continuous crossover is visible for $1\lesssim \sigma \lesssim 2$ with non-universal, $\sigma$-dependent values of $\lambda$. The performed Metropolis Monte Carlo simulations are primarily enabled by our novel algorithm for long-range interacting systems.

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• Physical ageing from generalised time-translation-invariance
• Short-time dynamics in phase-ordering kinetics
• Exact solution of the Glauber-Ising model on the finite-length semi-open chain