51 research outputs found
Time and length scales in spin glasses
We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy
phase. We briefly review the present theoretical understanding of the
spectacular phenomena observed in experiments and describe new numerical
results obtained in the first large-scale simulation of the nonequilibrium
dynamics of the three dimensional Heisenberg spin glass.Comment: Paper presented at "Highly Frustrated Magnetism 2003", Grenoble,
August 200
Fluctuation-dissipation relations in plaquette spin systems with multi-stage relaxation
We study aging dynamics in two non-disordered spin models with multi-spin
interactions, following a sudden quench to low temperature. The models are
relevant to the physics of supercooled liquids. Their low temperature dynamics
resemble those of kinetically constrained models, and obey dynamical scaling,
controlled by zero-temperature critical points. Dynamics in both models are
thermally activated, resulting in multi-stage relaxation towards equilibrium.
We study several two-time correlation and response functions. We find that
equilibrium fluctuation-dissipation relations are generically not satisfied
during the aging regime, but deviations from them are well described by
fluctuation-dissipation ratios, as found numerically in supercooled liquids.
These ratios are purely dynamic objects, containing information about the
nature of relaxation in the models. They are non-universal, and can even be
negative as a result of activated dynamics. Thus, effective temperatures are
not well-defined in these models.Comment: 29 pages, 10 fig
Real space application of the mean-field description of spin glass dynamics
The out of equilibrium dynamics of finite dimensional spin glasses is
considered from a point of view going beyond the standard `mean-field theory'
versus `droplet picture' debate of the last decades. The main predictions of
both theories concerning the spin glass dynamics are discussed. It is shown, in
particular, that predictions originating from mean-field ideas concerning the
violations of the fluctuation-dissipation theorem apply quantitatively,
provided one properly takes into account the role of the spin glass coherence
length which plays a central role in the droplet picture. Dynamics in a uniform
magnetic field is also briefly discussed.Comment: 4 pages, 4 eps figures. v2: published versio
Local excitations in mean field spin glasses
We address the question of geometrical as well as energetic properties of
local excitations in mean field Ising spin glasses. We study analytically the
Random Energy Model and numerically a dilute mean field model, first on
tree-like graphs, equivalent to a replica symmetric computation, and then
directly on finite connectivity random lattices. In the first model,
characterized by a discontinuous replica symmetry breaking, we found that the
energy of finite volume excitation is infinite whereas in the dilute mean field
model, described by a continuous replica symmetry breaking, it slowly decreases
with sizes and saturates at a finite value, in contrast with what would be
naively expected. The geometrical properties of these excitations are similar
to those of lattice animals or branched polymers. We discuss the meaning of
these results in terms of replica symmetry breaking and also possible relevance
in finite dimensional systems.Comment: 7 pages, 4 figures, accepted for publicatio
Non-equilibrium dynamics of spin facilitated glass models
We consider the dynamics of spin facilitated models of glasses in the
non-equilibrium aging regime following a sudden quench from high to low
temperatures. We briefly review known results obtained for the broad class of
kinetically constrained models, and then present new results for the behaviour
of the one-spin facilitated Fredrickson-Andersen and East models in various
spatial dimensions. The time evolution of one-time quantities, such as the
energy density, and the detailed properties of two-time correlation and
response functions are studied using a combination of theoretical approaches,
including exact mappings of master operators and reductions to integrable
quantum spin chains, field theory and renormalization group, and independent
interval and timescale separation methods. The resulting analytical predictions
are confirmed by means of detailed numerical simulations. The models we
consider are characterized by trivial static properties, with no finite
temperature singularities, but they nevertheless display a surprising variety
of dynamic behaviour during aging, which can be directly related to the
existence and growth in time of dynamic lengthscales. Well-behaved
fluctuation-dissipation ratios can be defined for these models, and we study
their properties in detail. We confirm in particular the existence of negative
fluctuation-dissipation ratios for a large number of observables. Our results
suggest that well-defined violations of fluctuation-dissipation relations, of a
purely dynamic origin and unrelated to the thermodynamic concept of effective
temperatures, could in general be present in non-equilibrium glassy materials.Comment: 72 pages, invited contribution to special issue of JSTAT on
"Principles of Dynamics of Nonequilibrium Systems" (Programme at Newton
Institute Cambridge). v2: New data added to Figs. 11, 23, 24, new Fig. 26 on
East model in d=3, minor improvements to tex
Non-linear susceptibilities of spherical models
The static and dynamic susceptibilities for a general class of mean field
random orthogonal spherical spin glass models are studied. We show how the
static and dynamical properties of the linear and nonlinear susceptibilities
depend on the behaviour of the density of states of the two body interaction
matrix in the neighbourhood of the largest eigenvalue. Our results are compared
with experimental results and also with those of the droplet theory of spin
glasses.Comment: 20 pages, 2 fig
Energetics of clusters in the two-dimensional Ising spin glass
We study numerically the properties of local low-energy excitations in the
two-dimensional Ising spin glass. Given the ground state, we determine the
lowest-lying connected cluster of flipped spins containing one given spin,
either with a fixed volume, or with a volume constrained to lie in a certain
range. Our aim is to understand corrections to the scaling predicted by the
droplet picture of spin glasses and to resolve contradictory results reported
in the literature for the stiffness exponent. We find no clear trace of
corrections to scaling, and the obtained stiffness exponent is in relatively
good agreement with standard domain wall calculations.Comment: 8 pages, 9 figure
Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
This review reports on the research done during the past years on violations
of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused
on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy
systems and the currently supporting knowledge gained from numerical simulation
studies. It covers a broad range of non-stationary aging and stationary driven
systems such as structural-glasses, spin-glasses, coarsening systems,
ferromagnetic models at criticality, trap models, models with entropy barriers,
kinetically constrained models, sheared systems and granular media. The review
is divided into four main parts: 1) An introductory section explaining basic
notions related to the existence of the FDT in equilibrium and its possible
extension to the glassy regime (QFDT), 2) A description of the basic analytical
tools and results derived in the framework of some exactly solvable models, 3)
A detailed report of the current evidence in favour of the QFDT and 4) A brief
digression on the experimental evidence in its favour. This review is intended
for inexpert readers who want to learn about the basic notions and concepts
related to the existence of the QFDT as well as for the more expert readers who
may be interested in more specific results.Comment: 120 pages, 37 figures. Topical review paper . Several typos and
misprints corrected, new references included and others updated. to be
published in J. Phys. A (Math. Gen.
Chirality scenario of the spin-glass ordering
Detailed account is given of the chirality scenario of experimental
spin-glass transitions. In this scenario, the spin glass order of weakly
anisotropic Heisenberg-like spin-glass magnets including canonical spin glasses
are essentially chirality driven. Recent numerical and experimental results are
discussed in conjunction with this scenario.Comment: Submitted to J. Phys. Soc. Japan "Special Issue on Frustration
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