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Reply to the Comment by L. Berthier and J.-P. Bouchaud, Phys. Rev. Lett. 90, 059701 (2003), also cond-mat/0209165, on our paper Phys. Rev. Lett. 89, 097201 (2002), also cond-mat/0203444
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The aging in a Heisenberg-like spin glass Ag(11 at% Mn) is investigated by measurements of the zero field cooled magnetic relaxation at a constant temperature after small temperature shifts $|Delta T/T_g| < 0.012$. A crossover from fully accumulative to non-accumulative aging is observed, and by converting time scales to length scales using the logarithmic growth law of the droplet model, we find a quantitative evidence that positive and negative temperature shifts cause an equivalent restart of aging (rejuvenation) in terms of dynamical length scales. This result supports the existence of a unique overlap length between a pair of equilibrium states in the spin glass system.
Domain-wall free-energy $delta F$, entropy $delta S$, and the correlation function, $C_{rm temp}$, of $delta F$ are measured independently in the four-dimensional $pm J$ Edwards-Anderson (EA) Ising spin glass. The stiffness exponent $theta$, the fractal dimension of domain walls $d_{rm s}$ and the chaos exponent $zeta$ are extracted from the finite-size scaling analysis of $delta F$, $delta S$ and $C_{rm temp}$ respectively well inside the spin-glass phase. The three exponents are confirmed to satisfy the scaling relation $zeta=d_{rm s}/2-theta$ derived by the droplet theory within our numerical accuracy. We also study bond chaos induced by random variation of bonds, and find that the bond and temperature perturbations yield the universal chaos effects described by a common scaling function and the chaos exponent. These results strongly support the appropriateness of the droplet theory for the description of chaos effect in the EA Ising spin glasses.
A recent interesting paper [Yucesoy et al. Phys. Rev. Lett. 109, 177204 (2012), arXiv:1206:0783] compares the low-temperature phase of the 3D Edwards-Anderson (EA) model to its mean-field counterpart, the Sherrington-Kirkpatrick (SK) model. The authors study the overlap distributions P_J(q) and conclude that the two models behave differently. Here we notice that a similar analysis using state-of-the-art, larger data sets for the EA model (generated with the Janus computer) leads to a very clear interpretation of the results of Yucesoy et al., showing that the EA model behaves as predicted by the replica symmetry breaking (RSB) theory.
In Phys. Rev. Lett. 110, 219701 (2013) [arXiv:1211.0843] Billoire et al. criticize the conclusions of our Letter [Phys. Rev. Lett. 109, 177204 (2012), arxiv:1206.0783]. They argue that considering the Edwards-Anderson and Sherrington-Kirkpatrick models at the same temperature is inappropriate and propose an interpretation based on the replica symmetry breaking theory. Here we show that the theory presented in the Comment does not explain our data on the Edwards-Anderson spin glass and we stand by our assertion that the low-temperature behavior of the Edwards-Anderson spin glass model does not appear to be mean-field like.
We find a dynamic effect in the non-equilibrium dynamics of a spin glass that closely parallels equilibrium temperature chaos. This effect, that we name dynamic temperature chaos, is spatially heterogeneous to a large degree. The key controlling quantity is the time-growing spin-glass coherence length. Our detailed characterization of dynamic temperature chaos paves the way for the analysis of recent and forthcoming experiments. This work has been made possible thanks to the most massive simulation to date of non-equilibrium dynamics, carried out on the Janus~II custom-built supercomputer.
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