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arXiv:1307.4998 · Physical Review E

Dynamical transition in the D=3 Edwards-Anderson spin glass in an external magnetic field

Marco Baity‐Jesi, R. A. Baños, Andrés De la Cruz, L. A. Fernández, Jose Miguel Gil-Narvion, A. Gordillo-Guerrero, D. Íñiguez, A. Maiorano, Filippo Mantovani, Enzo Marinari, Víctor Martín-Mayor, Jorge Monforte-Garcia, A. Muñoz Sudupe, Denis Navarro, Giorgio Parisi A, Sergio Perez-Gaviro, Marcello Pivanti, Federico Ricci‐Tersenghi, Juan Jesus Ruiz-Lorenzo, Sebastiano Fabio Schifano, Beatriz Seoane, Alfonso Tarancón, R. Tripiccione, David Yllanes

Published Mar 31, 2014• 43 citations

Abstract

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 field-programmable gate array (FPGAs), we have been able to reach times equivalent to 0.01 s 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.

DOI: 10.1103/physreve.89.032140

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We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards–Anderson spin glass in a field, using the Janus computer. A traditional analysis shows no signs of a phase transition. However, we encounter dramatic fluctuations in the behaviour of the model: averages over all the data only describe the behaviour of a small fraction of the data. 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 some of the measurements behave as the average, while the majority show 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.

Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field

h

are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature

T

. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal

h

. In comparison with this numerical result the field effect on real spin glasses is also discussed.

The out of equilibrium evolution for an Edwards‐Anderson spin glass is followed for a tenth of a second, a long enough time to let us make safe predictions about the behaviour at experimental scales. This work has been made possible by Janus, an FPGA based special purpose computer. We have thoroughly studied the spin glass correlation functions and the growth of the coherence length for L = 80 lattices in 3D. Our main conclusion is that these spin glasses follow noncoarsening dynamics, at least up to the experimentally relevant time scales.

First results of massive Monte Carlo simulations of the d=3 Ising spin glass with ± J bond distribution, performed on a fast special purpose computer, are discussed. Equilibrium static and dynamic correlation functions have been recorded for temperatures T/J=1.10 to 2.00. A qualitative change in the behavior of the system, and the best fits for the spin glass correlation length and relaxation time favor a continuous phase transition at Tc/J≊1.20±0.05. We find no evidence for the Tc=0 freezing picture.

First results of massive Monte Carlo simulations of the d=3 Ising spin glass with ± J bond distribution, performed on a fast special purpose computer, are discussed. Equilibrium static and dynamic correlation functions have been recorded for temperatures T/J=1.10 to 2.00. A qualitative change in the behavior of the system, and the best fits for the spin glass correlation length and relaxation time favor a continuous phase transition at Tc/J≊1.20±0.05. We find no evidence for the Tc=0 freezing picture.

Using the decay of the out equilibrium spin-spin correlation function we compute the equilibrium Edward-Anderson order parameter in the three dimensional binary Ising spin glass in the spin glass phase. We have checked that the Edward-Anderson order parameter computed from out of equilibrium numerical simulations follows with good precision the critical law as determined in experiments and in numerical studies at equilibrium. We have also studied the dependence of the order parameter with the lattice size. Finally we present a large time study of the scaling of the off-equilibrium fluctuation-dissipation relations.