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arXiv:cond-mat/9904321

Comment on "Numerical Study on Aging Dynamics in the 3D Ising Spin Glass Model"

Enzo Marinari, Giorgio Parisi A, Juan Jesus Ruiz-Lorenzo

Published Apr 22, 1999• 1 citation
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Abstract

We show that the dynamical behavior of the 3D Ising spin glass with Gaussian couplings is not compatible with a droplet dynamics. We show that this is implied from the data of reference cond-mat/9904143, that, when analyzed in an accurate way, give multiple evidences of this fact. Our study is based on the analysis of the overlap-overlap correlation function, at different values of the separation r and of the time t.

DOI
10.48550/arxiv.cond-mat/9904321

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Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of {\it effective stiffness} for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.
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By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature(TTT)-change protocols. Particularly, a TTT-shift protocol, in which a system is first quenched to and aged for a period tw1t_{\rm w1}tw1​ at a temperature T1T_1T1​, and subsequently aged at a new temperature T2T_2T2​ is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the TTT-change. We also found the relaxation of energy density and spin auto-correlation function during the TTT-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of T2T_2T2​ at around t2≃tw1(eff)t_2 \simeq t_{\rm w1}^{\rm (eff)}t2​≃tw1(eff)​ after the TTT-change, where tw1(eff)t_{\rm w1}^{\rm (eff)}tw1(eff)​ is an effective waiting time related with tw1t_{\rm w1}tw1​, but in the transient regime t2<tw1(eff)t_2 \lt t_{\rm w1}^{\rm (eff)}t2​<tw1(eff)​, adjustment of the population of thermally active droplets from that at T1T_1T1​ to T2T_2T2​ takes place very slowly. Implications of the results on aging phenomena in other TTT-change protocols such as TTT-cycling and continuous TTT-change with an intermittent stop observed by simulations as well as experiments are discussed.
In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field BBB. By using a new, powerful method, they determine an effective critical field BcB_cBc​ as a function of the lattice size LLL. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.