# Aging in the long-range Ising model

## TL;DR

This paper investigates aging phenomena in a two-dimensional long-range Ising model, revealing how interaction range influences aging dynamics and autocorrelation exponents through Monte Carlo simulations.

## Contribution

It provides the first detailed study of aging in long-range interacting systems, extending understanding beyond short-range models.

## Key findings

- Aging follows simple scaling across all studied interaction ranges.
- Autocorrelation exponents vary with interaction range, consistent with theoretical predictions.
- Finite-size effects are significant for very long-range interactions, affecting interpretation.

## Abstract

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with $\lambda=1.25$ in the effectively short-range regime, while for stronger long-range interactions the data are consistent with $\lambda=d/2=1$. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as sub-aging.