Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below $T_C$

Abstract

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 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 $a=0.27\pm 0.002$ for the scaling exponent of the response function in the $d=2$ Ising model quenched to below $T_C$, in agreement with previous results.

24 pages, 6 figures. Resubmitted version with improved discussions and figures

References in corpus (4)

• Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models
• Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance
• Ageing phenomena without detailed balance: the contact process
• On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance

Cited by in corpus (9)

• Nonlinear response and fluctuation dissipation relations
• Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model
• Dynamic fluctuations in unfrustrated systems: random walks, scalar fields and the Kosterlitz-Thouless phase
• Universality in three-dimensional Ising spin glasses: Nonequilibrium dynamics from Monte Carlo simulations
• Growth Kinetics and Aging Phenomena in a Frustrated System
• Dynamical response function of the disordered kinetic Ising model
• On the predictive power of Local Scale Invariance
• Effects of Frustration on Fluctuation-dissipation Relations
• Ageing in homogeneous systems at criticality