80 research outputs found
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
APE Results of Hadron Masses in Full QCD Simulations
We present numerical results obtained in full QCD with 2 flavors of Wilson
fermions. We discuss the relation between the phase of Polyakov loops and the
{\bf sea} quarks boundary conditions. We report preliminary results about the
HMC autocorrelation of the hadronic masses, on a lattice
volume, at with .Comment: 3 pages, compressed ps-file (uufiles), Contribution to Lattice 9
Measures of critical exponents in the four dimensional site percolation
Using finite-size scaling methods we measure the thermal and magnetic exponents of the site percolation in four dimensions, obtaining a value for the anomalous dimension very different from the results found in the literature. We also obtain the leading corrections-to-scaling exponent and, with great accuracy, the critical density
Non-renormalizability of the HMC algorithm
In lattice field theory, renormalizable simulation algorithms are attractive,
because their scaling behaviour as a function of the lattice spacing is
predictable. Algorithms implementing the Langevin equation, for example, are
known to be renormalizable if the simulated theory is. In this paper we show
that the situation is different in the case of the molecular-dynamics evolution
on which the HMC algorithm is based. More precisely, studying the phi^4 theory,
we find that the hyperbolic character of the molecular-dynamics equations leads
to non-local (and thus non-removable) ultraviolet singularities already at
one-loop order of perturbation theory.Comment: Plain TeX source, 23 pages, 3 figures included; v2: typos corrected,
agrees with published versio
Is trivial the antiferromagnetic RP(2) model in four dimensions?
We study the antiferromagnetic RP(2) model in four dimensions. We find a
second order transition with two order parameters, one ferromagnetic and the
other antiferromagnetic. The antiferromagnetic sector has mean-field critical
exponents and a renormalized coupling which goes to zero in the continuum
limit. The exponents of the ferromagnetic channel are not the mean-field ones,
but the difference can be interpreted as logarithmic corrections. We perform a
detailed analysis of these corrections and conclude the triviality of the
continuum limit of this model.Comment: 21 pages, 5 figures, LaTeX2
An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature
Using the dedicated computer Janus, we follow the nonequilibrium dynamics of
the Ising spin glass in three dimensions for eleven orders of magnitude. The
use of integral estimators for the coherence and correlation lengths allows us
to study dynamic heterogeneities and the presence of a replicon mode and to
obtain safe bounds on the Edwards-Anderson order parameter below the critical
temperature. We obtain good agreement with experimental determinations of the
temperature-dependent decay exponents for the thermoremanent magnetization.
This magnitude is observed to scale with the much harder to measure coherence
length, a potentially useful result for experimentalists. The exponents for
energy relaxation display a linear dependence on temperature and reasonable
extrapolations to the critical point. We conclude examining the time growth of
the coherence length, with a comparison of critical and activated dynamics.Comment: 38 pages, 26 figure
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
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