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

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.