35 research outputs found
Out-of-equilibrium thermodynamic relations in systems with aging and slow relaxation
The experimental time scale dependence of thermodynamic relations in
out-of-equilibrium systems with aging phenomena is investigated theoretically
by using only aging properties of the two-time correlation functions and the
generalized fluctuation-dissipation theorem (FDT). We show that there are two
experimental time regimes characterized by different thermal properties. In the
first regime where the waiting time is much longer than the measurement time,
the principle of minimum work holds even though a system is out of equilibrium.
In the second regime where both the measurement time and the waiting time are
long, the thermal properties are completely different from properties in
equilibrium. For the single-correlation-scale systems such as -spin
spherical spin-glasses, contrary to a fundamental assumption of thermodynamics,
the work done in an infinitely slow operation depends on the path of change of
the external field even when the waiting time is infinite. On the other hand,
for the multi-correlation-scale systems such as Sherrington-Kirkpatrick model,
the work done in an infinitely slow operation is independent of the path. Our
results imply that in order to describe thermodynamic properties of systems
with aging it is essential to consider the experimental time scales and history
of a system as a state variable is necessary.Comment: 28 pages(REVTeX), 4 figure(EPS). To be published in Phys. Rev.
String Propagator: a Loop Space Representation
The string quantum kernel is normally written as a functional sum over the
string coordinates and the world--sheet metrics. As an alternative to this
quantum field--inspired approach, we study the closed bosonic string
propagation amplitude in the functional space of loop configurations. This
functional theory is based entirely on the Jacobi variational formulation of
quantum mechanics, {\it without the use of a lattice approximation}. The
corresponding Feynman path integral is weighed by a string action which is a
{\it reparametrization invariant} version of the Schild action. We show that
this path integral formulation is equivalent to a functional ``Schrodinger''
equation defined in loop--space. Finally, for a free string, we show that the
path integral and the functional wave equation are {\it exactly } solvable.Comment: 15 pages, no figures, ReVTeX 3.
Ground state non-universality in the random field Ising model
Two attractive and often used ideas, namely universality and the concept of a
zero temperature fixed point, are violated in the infinite-range random-field
Ising model. In the ground state we show that the exponents can depend
continuously on the disorder and so are non-universal. However, we also show
that at finite temperature the thermal order parameter exponent one half is
restored so that temperature is a relevant variable. The broader implications
of these results are discussed.Comment: 4 pages 2 figures, corrected prefactors caused by a missing factor of
two in Eq. 2., added a paragraph in conclusions for clarit
About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass
Recently, it has been conjectured that the statistics of extremes is of
relevance for a large class of correlated system. For certain probability
densities this predicts the characteristic large fall-off behavior
, . Using a multicanonical Monte Carlo technique,
we have calculated the Parisi overlap distribution for the
three-dimensional Edward-Anderson Ising spin glass at and below the critical
temperature, even where is exponentially small. We find that a
probability distribution related to extreme order statistics gives an excellent
description of over about 80 orders of magnitude.Comment: 4 pages RevTex, 3 figure
Critical exponents in Ising spin glasses
We determine accurate values of ordering temperatures and critical exponents
for Ising Spin Glass transitions in dimension 4, using a combination of finite
size scaling and non-equilibrium scaling techniques. We find that the exponents
and vary with the form of the interaction distribution, indicating
non-universality at Ising spin glass transitions. These results confirm
conclusions drawn from numerical data for dimension 3.Comment: 6 pages, RevTeX (or Latex, etc), 10 figures, Submitted to PR
Spin and density overlaps in the frustrated Ising lattice gas
We perform large scale simulations of the frustrated Ising lattice gas, a
three-dimensional lattice model of a structural glass, using the parallel
tempering technique. We evaluate the spin and density overlap distributions,
and the corresponding non-linear susceptibilities, as a function of the
chemical potential. We then evaluate the relaxation functions of the spin and
density self-overlap, and study the behavior of the relaxation times. The
results suggest that the spin variables undergo a transition very similar to
the one of the Ising spin glass, while the density variables do not show any
sign of transition at the same chemical potential. It may be that the density
variables undergo a transition at a higher chemical potential, inside the phase
where the spins are frozen.Comment: 7 pages, 10 figure
Constrained spin dynamics description of random walks on hierarchical scale-free networks
We study a random walk problem on the hierarchical network which is a
scale-free network grown deterministically. The random walk problem is mapped
onto a dynamical Ising spin chain system in one dimension with a nonlocal spin
update rule, which allows an analytic approach. We show analytically that the
characteristic relaxation time scale grows algebraically with the total number
of nodes as . From a scaling argument, we also show the
power-law decay of the autocorrelation function C_{\bfsigma}(t)\sim
t^{-\alpha}, which is the probability to find the Ising spins in the initial
state {\bfsigma} after time steps, with the state-dependent non-universal
exponent . It turns out that the power-law scaling behavior has its
origin in an quasi-ultrametric structure of the configuration space.Comment: 9 pages, 6 figure
Universality of Frequency and Field Scaling of the Conductivity Measured by Ac-Susceptibility of a Ybco-Film
Utilizing a novel and exact inversion scheme, we determine the complex linear
conductivity from the linear magnetic ac-susceptibility
which has been measured from 3\,mHz to 50\,MHz in fields between 0.4\,T and
4\,T applied parallel to the c-axis of a 250\,nm thin disk. The frequency
derivative of the phase and the dynamical scaling of
above and below provide clear evidence for a
continuous phase transition at to a generic superconducting state. Based
on the vortex-glass scaling model, the resulting critical exponents and
are close to those frequently obtained on films by other means and
associated with an 'isotropic' vortex glass. The field effect on
can be related to the increase of the glass coherence length,
.Comment: 8 pages (5 figures upon request), revtex 3.0, APK.94.01.0
Properties of the random field Ising model in a transverse magnetic field
We consider the effect of a random longitudinal field on the Ising model in a
transverse magnetic field. For spatial dimension , there is at low
strength of randomness and transverse field, a phase with true long range order
which is destroyed at higher values of the randomness or transverse field. The
properties of the quantum phase transition at zero temperature are controlled
by a fixed point with no quantum fluctuations. This fixed point also controls
the classical finite temperature phase transition in this model. Many critical
properties of the quantum transition are therefore identical to those of the
classical transition. In particular, we argue that the dynamical scaling is
activated, i.e, the logarithm of the diverging time scale rises as a power of
the diverging length scale
A Percolation-Theoretic Approach to Spin Glass Phase Transitions
The magnetically ordered, low temperature phase of Ising ferro- magnets is
manifested within the associated Fortuin-Kasteleyn (FK) random cluster
representation by the occurrence of a single positive density percolating
cluster. In this paper, we review our recent work on the percolation signature
for Ising spin glass ordering -- both in the short-range Edwards-Anderson (EA)
and infinite-range Sherrington-Kirkpatrick (SK) models -- within a two-replica
FK representation and also in the different Chayes-Machta-Redner two-replica
graphical representation. Numerical studies of the EA model in
dimension three and rigorous results for the SK model are consistent in
supporting the conclusion that the signature of spin-glass order in these
models is the existence of a single percolating cluster of maximal density
normally coexisting with a second percolating cluster of lower density.Comment: Based on lectures given at the 2007 Paris Summer School "Spin
Glasses." 12 pages, 3 figure