39 research outputs found
Comment on "Evidence of Non-Mean-Field-Like Low-Temperature Behavior in the Edwards-Anderson Spin-Glass Model"
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.Comment: Version accepted for publication in PRL. 1 page, 1 figur
Numerical construction of the Aizenman-Wehr metastate
Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d ¼ 3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a dispersed metastate, supported on many thermodynamic states
Matching microscopic and macroscopic responses in glasses
We first reproduce on the Janus and Janus II computers a milestone experiment
that measures the spin-glass coherence length through the lowering of
free-energy barriers induced by the Zeeman effect. Secondly we determine the
scaling behavior that allows a quantitative analysis of a new experiment
reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett.
118, 157203 (2017)]. The value of the coherence length estimated through the
analysis of microscopic correlation functions turns out to be quantitatively
consistent with its measurement through macroscopic response functions.
Further, non-linear susceptibilities, recently measured in glass-forming
liquids, scale as powers of the same microscopic length.Comment: 6 pages, 4 figure
The Mpemba effect in spin glasses is a persistent memory effect
The Mpemba effect occurs when a hot system cools faster than an initially
colder one, when both are refrigerated in the same thermal reservoir. Using the
custom built supercomputer Janus II, we study the Mpemba effect in spin glasses
and show that it is a non-equilibrium process, governed by the coherence length
\xi of the system. The effect occurs when the bath temperature lies in the
glassy phase, but it is not necessary for the thermal protocol to cross the
critical temperature. In fact, the Mpemba effect follows from a strong
relationship between the internal energy and \xi that turns out to be a
sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents
itself as an intriguing new avenue for the experimental study of the coherence
length in supercooled liquids and other glass formers.Comment: Version accepted for publication in PNAS. 6 pages, 7 figure
The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
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.Comment: 42 pages, 19 figures. Minor changes and added figure (results
unchanged
Critical parameters of the three-dimensional Ising spin glass
We report a high-precision finite-size scaling study of the critical behavior
of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass).
We have thermalized lattices up to L=40 using the Janus dedicated computer. Our
analysis takes into account leading-order corrections to scaling. We obtain Tc
= 1.1019(29) for the critical temperature, \nu = 2.562(42) for the thermal
exponent, \eta = -0.3900(36) for the anomalous dimension and \omega = 1.12(10)
for the exponent of the leading corrections to scaling. Standard (hyper)scaling
relations yield \alpha = -5.69(13), \beta = 0.782(10) and \gamma = 6.13(11). We
also compute several universal quantities at Tc.Comment: 9 pages, 5 figure
On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance
The frequency-dependent scaling of the dispersive and dissipative parts of
the alternating susceptibility is studied for spin glasses at criticality. An
extension of the usual -scaling is proposed. Simulational data from
the three-dimensional Ising spin glass agree with this new scaling form and
moreover reproduce well the scaling functions explicitly calculated for systems
satisfying local scale-invariance. There is also a qualitative agreement with
existing experimental data.Comment: 19 pages, 2 figures, to appear in special issue of J. Phys. Cond.
Matt. dedicated to Lothar Schaefer on the occasion of his 60th birthday,
final form with IOP macro
Aging rate of spin glasses from simulations matches experiments
Experiments on spin glasses can now make precise measurements of the exponent
governing the growth of glassy domains, while our computational
capabilities allow us to make quantitative predictions for experimental scales.
However, experimental and numerical values for have differed. We use new
simulations on the Janus II computer to resolve this discrepancy, finding a
time-dependent , which leads to the experimental value through mild
extrapolations. Furthermore, theoretical insight is gained by studying a
crossover between the and fixed points.Comment: Version accepted for publication in PRL. 12 pages, 9 figure
Temperature chaos is present in off-equilibrium spin-glass dynamics
Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ¿. Indeed, an emerging length-scale ¿* rules the crossover from weak (at ¿ « ¿*) to strong chaos (¿ » ¿*). Extrapolations of ¿* to relevant experimental conditions are provided. © 2021, The Author(s)