Correction to scaling in the response function of the 2d kinetic Ising model

TL;DR

This study investigates the aging response function in the 2D kinetic Ising model, revealing deviations from simple scaling and proposing a correction to scaling that aligns well with numerical data and analytical predictions.

Contribution

The paper introduces a correction to the scaling form of the aging response function in the 2D kinetic Ising model and provides an analytical expression that matches numerical results.

Findings

Scaling form $R_{ag}(t,s)=s^{-(1+a)}f(t/s)$ does not hold strictly.

A correction to scaling improves the agreement between theory and numerical data.

Zero field cooled susceptibility is less sensitive to correction effects.

Abstract

The aging part $R_{ag}(t,s)$ of the impulsive response function of the two dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing a new algorithm without the imposition of the external field. We find that the simple scaling form $R_{ag}(t,s)=s^{-(1+a)}f(t/s)$, which is usually believed to hold in the aging regime, is not obeyed. We analyse the data assuming the existence of a correction to scaling. We find $a=0.273 \pm 0.006$, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function $f(t/s)$ and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for $R_{ag}(t,s)$. This gives a satisfactory qualitative agreement with the numerical data for $R_{ag}(t,s)$ and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in $R_{ag}(t,s)$, making this quantity the most convenient for the study of the asymptotic scaling properties.