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In order to check on a recent suggestion that local scale invariance[M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when thedynamics is of Gaussian nature, we have carried out the measurement of theresponse function in the kinetic Ising model with Glauber dynamics quenched to$T_C$ in $d=4$, where Gaussian behavior is expected to apply, and in the twoother cases of the $d=2$ model quenched to $T_C$ and to below $T_C$, whereinstead deviations from Gaussian behavior are expected to appear. We find thatin the $d=4$ case there is an excellent agreement between the numerical data,the local scale invariance prediction and the analytical Gaussianapproximation. No logarithmic corrections are numerically detected. Conversely,in the $d=2$ cases, both in the quench to $T_C$ and to below $T_C$, sizabledeviations of the local scale invariance behavior from the numerical data areobserved. These results do support the idea that local scale invariance mightmiss to capture the non Gaussian features of the dynamics. The considerableprecision needed for the comparison has been achieved through the use of a fastnew algorithm for the measurement of the response function without applying theexternal field. From these high quality data we obtain $a=0.27 \pm 0.002$ forthe scaling exponent of the response function in the $d=2$ Ising model quenchedto below $T_C$, in agreement with previous results.Comment: 24 pages, 6 figures. Resubmitted version with improved discussions  and figure

physical review. e, statistical, nonlinear and soft matter physics

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Test of local scale invariance from the direct measurement of the response function in the Ising model quenched to and belowTC