1,410 research outputs found
The spherical spin glass model: an exactly solvable model for glass to spin-glass transition
We present the full phase diagram of the spherical spin glass model
with . The main outcome is the presence of a new phase with both
properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models,
e.g, the Sherrington-Kirkpatrick model, and those of One Replica Symmetry
Breaking (1RSB). The phase, which separates a 1RSB phase from FRSB phase, is
described by an order parameter function with a continuous part (FRSB)
for and a discontinuous jump (1RSB) at . This phase has a finite
complexity which leads to different dynamic and static properties.Comment: 5 pages, 2 figure
Inherent Structures, Configurational Entropy and Slow Glassy Dynamics
We give a short introduction to the inherent structure approach, with
particular emphasis on the Stillinger and Weber decomposition, of glassy
systems. We present some of the results obtained in the framework of spin-glass
models and Lennard-Jones glasses. We discuss how to generalize the standard
Stillinger and Weber approach by including the entropy of inherent structures.
Finally we discuss why this approach is probably insufficient to describe the
behavior of some kinetically constrained models.Comment: 16 pages, 8 figures, Contribution to the ESF SPHINX meeting `Glassy
behaviour of kinetically constrained models' (Barcelona, March 22-25, 2001
Frequency-domain study of relaxation in a spin glass model for the structural glass transition
We have computed the time-dependent susceptibility for the finite-size
mean-field Random Orthogonal model (ROM). We find that for temperatures above
the mode-coupling temperature the imaginary part of the susceptibility
obeys the scaling forms proposed for glass-forming liquids.
Furthermore, as the temperature is lowered the peak frequency of
decreases following a Vogel-Fulcher law with a critical temperature remarkably
close to the known critical temperature where the configurational entropy
vanishes.Comment: 7 pages, 4 figures, epl LaTeX packag
Replica symmetry breaking in long-range glass models without quenched disorder
We discuss mean field theory of glasses without quenched disorder focusing on
the justification of the replica approach to thermodynamics. We emphasize the
assumptions implicit in this method and discuss how they can be verified. The
formalism is applied to the long range Ising model with orthogonal coupling
matrix. We find the one step replica-symmetry breaking solution and show that
it is stable in the intermediate temperature range that includes the glass
state but excludes very low temperatures. At very low temperatures this
solution becomes unstable and this approach fails.Comment: 6 pages, 2 figure
Characterization of a periodically driven chaotic dynamical system
We discuss how to characterize the behavior of a chaotic dynamical system
depending on a parameter that varies periodically in time. In particular, we
study the predictability time, the correlations and the mean responses, by
defining a local--in--time version of these quantities. In systems where the
time scale related to the time periodic variation of the parameter is much
larger than the ``internal'' time scale, one has that the local quantities
strongly depend on the phase of the cycle. In this case, the standard global
quantities can give misleading information.Comment: 15 pages, Revtex 2.0, 8 figures, included. All files packed with
uufile
The spherical 2+p spin glass model: an analytically solvable model with a glass-to-glass transition
We present the detailed analysis of the spherical s+p spin glass model with
two competing interactions: among p spins and among s spins. The most
interesting case is the 2+p model with p > 3 for which a very rich phase
diagram occurs, including, next to the paramagnetic and the glassy phase
represented by the one step replica symmetry breaking ansatz typical of the
spherical p-spin model, other two amorphous phases. Transitions between two
contiguous phases can also be of different kind. The model can thus serve as
mean-field representation of amorphous-amorphous transitions (or transitions
between undercooled liquids of different structure). The model is analytically
solvable everywhere in the phase space, even in the limit where the infinite
replica symmetry breaking ansatz is required to yield a thermodynamically
stable phase.Comment: 21 pages, 18 figure
Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses
We investigate the inherent structure (IS) dynamics of mean-field {\it
finite-size} spin-glass models whose high-temperature dynamics is described in
the thermodynamic limit by the schematic Mode Coupling Theory for super-cooled
liquids. Near the threshold energy the dynamics is ruled by activated processes
which induce a logarithmic slow relaxation. We show the presence of aging in
both the IS correlation and integrated response functions and check the
validity of the one-step replica symmetry breaking scenario in the presence of
activated processes. Our work shows: 1) The violation of the
fluctuation-dissipation theorem is given by the configurational entropy, 2) The
intermediate time regime () in mean-field theory automatically
includes activated processes opening the way to analytically investigate
activated processes by computing corrections beyond mean-field.Comment: 8 pages, 3 postscript figures, EPL format, improved versio
Observable Dependent Quasi-Equilibrium in Slow Dynamics
We present examples demonstrating that quasi-equilibrium
fluctuation-dissipation behavior at short time differences is not a generic
feature of systems with slow non-equilibrium dynamics. We analyze in detail the
non-equilibrium fluctuation-dissipation ratio X(t,tw) associated with a
defect-pair observable in the Glauber-Ising spin chain. It turns out that throughout the short-time regime and in particular X(tw,tw) = 3/4 for
. The analysis is extended to observables detecting defects at a
finite distance from each other, where similar violations of quasi-equilibrium
behaviour are found. We discuss our results in the context of metastable
states, which suggests that a violation of short-time quasi-equilibrium
behavior could occur in general glassy systems for appropriately chosen
observables.Comment: 17 pages, 5 figures; substantially improved version of
cond-mat/040571
Random bond Ising chain in a transverse magnetic field: A finite-size scaling analysis
We investigate the zero-temperature quantum phase transition of the random
bond Ising chain in a transverse magnetic field. Its critical properties are
identical to those of the McCoy-Wu model, which is a classical Ising model in
two dimensions with layered disorder. The latter is studied via Monte Carlo
simulations and transfer matrix calculations and the critical exponents are
determined with a finite-size scaling analysis. The magnetization and
susceptibility obey conventional rather than activated scaling. We observe that
the order parameter-- and correlation function--probability distribution show a
nontrivial scaling near the critical point which implies a hierarchy of
critical exponents associated with the critical behavior of the generalized
correlation lengths.Comment: RevTeX 13 pages + 4 figures (appended as uuencoded compressed
tar-file), THP61-9
Statistical Mechanics of Shell Models for 2D-Turbulence
We study shell models that conserve the analogues of energy and enstrophy,
hence designed to mimic fluid turbulence in 2D. The main result is that the
observed state is well described as a formal statistical equilibrium, closely
analogous to the approach to two-dimensional ideal hydrodynamics of Onsager,
Hopf and Lee. In the presence of forcing and dissipation we observe a forward
flux of enstrophy and a backward flux of energy. These fluxes can be understood
as mean diffusive drifts from a source to two sinks in a system which is close
to local equilibrium with Lagrange multipliers (``shell temperatures'')
changing slowly with scale. The dimensional predictions on the power spectra
from a supposed forward cascade of enstrophy, and from one branch of the formal
statistical equilibrium, coincide in these shell models at difference to the
corresponding predictions for the Navier-Stokes and Euler equations in 2D. This
coincidence have previously led to the mistaken conclusion that shell models
exhibit a forward cascade of enstrophy.Comment: 25 pages + 9 figures, TeX dialect: RevTeX 3.
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