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Register a new userDynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
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We study the off-equilibrium dynamics of the three-dimensional Ising spin glass in the presence of an external magnetic field. We have performed simulations both at fixed temperature and with an annealing protocol. Thanks to the Janus special-purpose computer, based on FPGAs, we have been able to reach times equivalent to 0.01 seconds in experiments. We have studied the system relaxation both for high and for low temperatures, clearly identifying a dynamical transition point. This dynamical temperature is strictly positive and depends on the external applied magnetic field. We discuss different possibilities for the underlying physics, which include a thermodynamical spin-glass transition, a mode-coupling crossover or an interpretation reminiscent of the random first-order picture of structural glasses.
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The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.
In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.
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.
We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic Stability and Overlap Equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks
We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed.
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