43 research outputs found
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
Thermodynamic glass transition in a spin glass without time-reversal symmetry
Spin glasses are a longstanding model for the sluggish dynamics that appears
at the glass transition. However, spin glasses differ from structural glasses
for a crucial feature: they enjoy a time reversal symmetry. This symmetry can
be broken by applying an external magnetic field, but embarrassingly little is
known about the critical behaviour of a spin glass in a field. In this context,
the space dimension is crucial. Simulations are easier to interpret in a large
number of dimensions, but one must work below the upper critical dimension
(i.e., in d<6) in order for results to have relevance for experiments. Here we
show conclusive evidence for the presence of a phase transition in a
four-dimensional spin glass in a field. Two ingredients were crucial for this
achievement: massive numerical simulations were carried out on the Janus
special-purpose computer, and a new and powerful finite-size scaling method.Comment: 10 pages, 6 figure
Critical Behavior of Three-Dimensional Disordered Potts Models with Many States
We study the 3D Disordered Potts Model with p=5 and p=6. Our numerical
simulations (that severely slow down for increasing p) detect a very clear spin
glass phase transition. We evaluate the critical exponents and the critical
value of the temperature, and we use known results at lower values to
discuss how they evolve for increasing p. We do not find any sign of the
presence of a transition to a ferromagnetic regime.Comment: 9 pages and 9 Postscript figures. Final version published in J. Stat.
Mec
Nature of the spin-glass phase at experimental length scales
We present a massive equilibrium simulation of the three-dimensional Ising
spin glass at low temperatures. The Janus special-purpose computer has allowed
us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc.
We demonstrate the relevance of equilibrium finite-size simulations to
understand experimental non-equilibrium spin glasses in the thermodynamical
limit by establishing a time-length dictionary. We conclude that
non-equilibrium experiments performed on a time scale of one hour can be
matched with equilibrium results on L=110 lattices. A detailed investigation of
the probability distribution functions of the spin and link overlap, as well as
of their correlation functions, shows that Replica Symmetry Breaking is the
appropriate theoretical framework for the physically relevant length scales.
Besides, we improve over existing methodologies to ensure equilibration in
parallel tempering simulations.Comment: 48 pages, 19 postscript figures, 9 tables. Version accepted for
publication in the Journal of Statistical Mechanic
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
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.Comment: Version accepted for publication in Communication Physics 10 pages, 9
figure