Comment on Numerical Study on Aging Dynamics in the 3D Ising Spin Glass Model
نویسندگان
چکیده
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 [1], 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. In a very interesting paper [1] Komori, Yoshino and Takayama discuss the dynamical behavior of the three dimensional (3D) Edwards Anderson (EA) Ising Spin Glass with Gaussian couplings. A number of very accurate numerical evidences are used to try to determine if the 3D EA model behaves in analogy to the Replica Symmetry Broken (RSB) solution of the Mean Field Sherrington Kirkpatrick model [2], or if its behavior is the one typical of coarsening of domain walls [3], in agreement with a picture of separated droplets [4]. The evidences presented in [1] can seem at first view to have mixed signs. For sake of completeness let us try to summarize all the available evidence. As it is well explained in the paper [1] some of the findings are obviously devastating for a droplet picture. The free energy barriers BL found on a lattice of linear size L do not grow with L like L, but with a logarithmic dependence BL ∝ log(L) (this was already 1 observed by Kisker, Rieger, Santen and Schreckenberg in [5]). Secondly, at variance with the droplet picture, the width of the distribution of the free energy barriers instead of increasing with L turns out to be remarkably constant. These two features do not have any problem with the RSB picture. Two more findings are not in contradiction with any of the two exemplar behaviors. The relaxation process has an Arrhenius-type form, with the characteristic time of the form τ = τ0 exp (
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تاریخ انتشار 1999