13 research outputs found
Low temperature spin glass fluctuations: expanding around a spherical approximation
The spin glass behavior near zero temperature is a complicated matter. To get
an easier access to the spin glass order parameter and, at the same
time, keep track of , its matrix aspect, and hence of the Hessian
controlling stability, we investigate an expansion of the replicated free
energy functional around its ``spherical'' approximation. This expansion is
obtained by introducing a constraint-field and a (double) Legendre Transform
expressed in terms of spin correlators and constraint-field correlators. The
spherical approximation has the spin fluctuations treated with a global
constraint and the expansion of the Legendre Transformed functional brings them
closer and closer to the Ising local constraint. In this paper we examine the
first contribution of the systematic corrections to the spherical starting
point.Comment: 16 pages, 2 figure
Frozen capillary waves on glass surfaces: an AFM study
Using atomic force microscopy on silica and float glass surfaces, we give
evidence that the roughness of melted glass surfaces can be quantitatively
accounted for by frozen capillary waves. In this framework the height spatial
correlations are shown to obey a logarithmic scaling law; the identification of
this behaviour allows to estimate the ratio where is the
Boltzmann constant, the interface tension and the temperature
corresponding to the ``freezing'' of the capillary waves. Variations of
interface tension and (to a lesser extent) temperatures of annealing treatments
are shown to be directly measurable from a statistical analysis of the
roughness spectrum of the glass surfaces
Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses
Using the results of large scale numerical simulations we study the
probability distribution of the pseudo critical temperature for the
three-dimensional Edwards-Anderson Ising spin glass and for the fully connected
Sherrington-Kirkpatrick model. We find that the behavior of our data is nicely
described by straightforward finite-size scaling relations.Comment: 23 pages, 9 figures. Version accepted for publication in J. Stat.
Mec
Mode-Coupling as a Landau Theory of the Glass Transition
We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau
theory, formulated as an expansion of the exact dynamical equations in the
difference between the correlation function and its plateau value. This sheds
light on the universality of MCT predictions. While our expansion generates
higher order non-local corrections that modify the standard MCT equations, we
find that the square root singularity of the order parameter, the scaling
function in the \beta regime and the functional relation between the exponents
defining the \alpha and \beta timescales are universal and left intact by these
corrections.Comment: 6 pages, 1 figure, submitted to EPL; corrected typos in the abstract;
corrected minor typo in reference
Predictive power of MCT: Numerics and Finite size scaling for a mean field spin glass
The aim of this paper is to test numerically the predictions of the Mode
Coupling Theory (MCT) of the glass transition and study its finite size scaling
properties in a model with an exact MCT transition, which we choose to be the
fully connected Random Orthogonal Model. Surprisingly, some predictions are
verified while others seem clearly violated, with inconsistent values of some
MCT exponents. We show that this is due to strong pre-asymptotic effects that
disappear only in a surprisingly narrow region around the critical point. Our
study of Finite Size Scaling (FSS) show that standard theory valid for pure
systems fails because of strong sample to sample fluctuations. We propose a
modified form of FSS that accounts well for our results. {\it En passant,} we
also give new theoretical insights about FSS in disordered systems above their
upper critical dimension. Our conclusion is that the quantitative predictions
of MCT are exceedingly difficult to test even for models for which MCT is
exact. Our results highlight that some predictions are more robust than others.
This could provide useful guidance when dealing with experimental data.Comment: 37 pages, 19 figure
Dynamical behavior of a lattice glass model on a random graph: Comparison with the Mode Coupling Theory
Random transverse field Ising model on the Cayley tree: analysis via boundary strong disorder renormalization
Random transverse field Ising model in dimension d
For the quantum Ising model with ferromagnetic random couplings
and random transverse fields at zero temperature in finite dimensions
, we consider the lowest-order contributions in perturbation theory in
to obtain some information on the statistics of various
observables in the disordered phase. We find that the two-point correlation
scales as : , where
is the typical correlation length, is a random variable, and
coincides with the droplet exponent of the
Directed Polymer with transverse directions. Our main conclusions are
(i) whenever , the quantum model is governed by an Infinite-Disorder
fixed point : there are two distinct correlation length exponents related by
; the distribution of the local susceptibility
presents the power-law tail where vanishes as , so that
the averaged local susceptibility diverges in a finite neighborhood
before criticality (Griffiths phase) ; the dynamical exponent diverges near
criticality as (ii) in dimensions ,
any infinitesimal disorder flows towards this Infinite-Disorder fixed point
with (for instance and )
(iii) in finite dimensions , a finite disorder strength is necessary to
flow towards the Infinite-Disorder fixed point with (for instance
), whereas a Finite-Disorder fixed point remains
possible for a small enough disorder strength. For the Cayley tree of effective
dimension where , we discuss the similarities and
differences with the case of finite dimensions.Comment: 22 pages, v2=final versio