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

In order to check on a recent suggestion that local scale invariance [M. Henkel , Phys. Rev. Lett. 87, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response 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 two other cases of the d=2 model quenched to T-C and to below T-C, where instead deviations from Gaussian behavior are expected to appear. We find that in the d=4 case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the d=2 cases, both in the quench to T-C and to below T-C, sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non-Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain a=0.27 +/- 0.002 for the scaling exponent of the response function in the d=2 Ising model quenched to below T-C, in agreement with previous results.