Finite-Size Scaling Study of Aging during Coarsening in Non-Conserved Ising Model: The case of zero temperature quench

TL;DR

This study investigates aging and domain growth in the zero-temperature quenched ferromagnetic Ising model in 2D and 3D, revealing power-law scaling, temperature effects in 3D, and confirmation of the Lifshitz-Allen-Cahn law.

Contribution

It provides a finite-size scaling analysis of aging during coarsening in the zero-temperature Ising model, highlighting differences between 2D and 3D behaviors and confirming domain growth laws.

Findings

Scaling of autocorrelations with domain size ratio is power-law.

No temperature dependence observed in 2D.

In 3D, zero-temperature results differ from high-temperature cases and violate bounds.

Abstract

Following quenches from random initial configurations to zero temperature, we study aging during evolution of the ferromagnetic (nonconserved) Ising model towards equilibrium, via Monte Carlo simulations of very large systems, in space dimensions $d=2$ and $3$. Results for the two-time autocorrelations, obtained by using different acceptance probabilities for the spin-flip trial moves, are in agreement with each other. We demonstrate the scaling of this quantity with respect to $\ell/\ell_w$, where $\ell$ and $\ell_w$ are the average domain sizes at $t$ and $t_w$ $(\leqslant t)$, the observation and waiting times, respectively. The scaling functions are shown to be of power-law type for $\ell/\ell_{w} \rightarrow \infty$. The exponents of these power-laws have been estimated via the finite-size scaling analyses and discussed with reference to the available results from non-zero temperatures. While in $d=2$ we do not observe any temperature dependence, in the case of $d=3$ the outcome for quench to zero temperature is very different from the available results for high temperature and violates a lower bound, which we explain via structural consideration. We also present results on the freezing phenomena that this model exhibits at zero temperature. Furthermore, from simulations of extremely large system, thereby avoiding the freezing effect, it has been confirmed that the growth of average domain size in $d=3$, that remained a puzzle in the literature, follows the Lifshitz-Allen-Cahn law in the asymptotic limit.