409 research outputs found
Relaxation properties in a lattice gas model with asymmetrical particles
We study the relaxation process in a two-dimensional lattice gas model, where
the interactions come from the excluded volume. In this model particles have
three arms with an asymmetrical shape, which results in geometrical frustration
that inhibits full packing. A dynamical crossover is found at the arm
percolation of the particles, from a dynamical behavior characterized by a
single step relaxation above the transition, to a two-step decay below it.
Relaxation functions of the self-part of density fluctuations are well fitted
by a stretched exponential form, with a exponent decreasing when the
temperature is lowered until the percolation transition is reached, and
constant below it. The structural arrest of the model seems to happen only at
the maximum density of the model, where both the inverse diffusivity and the
relaxation time of density fluctuations diverge with a power law. The dynamical
non linear susceptibility, defined as the fluctuations of the self-overlap
autocorrelation, exhibits a peak at some characteristic time, which seems to
diverge at the maximum density as well.Comment: 7 pages and 9 figure
Percolation and cluster Monte Carlo dynamics for spin models
A general scheme for devising efficient cluster dynamics proposed in a
previous letter [Phys.Rev.Lett. 72, 1541 (1994)] is extensively discussed. In
particular the strong connection among equilibrium properties of clusters and
dynamic properties as the correlation time for magnetization is emphasized. The
general scheme is applied to a number of frustrated spin model and the results
discussed.Comment: 17 pages LaTeX + 16 figures; will appear in Phys. Rev.
Number of spanning clusters at the high-dimensional percolation thresholds
A scaling theory is used to derive the dependence of the average number
of spanning clusters at threshold on the lattice size L. This number should
become independent of L for dimensions d<6, and vary as log L at d=6. The
predictions for d>6 depend on the boundary conditions, and the results there
may vary between L^{d-6} and L^0. While simulations in six dimensions are
consistent with this prediction (after including corrections of order loglog
L), in five dimensions the average number of spanning clusters still increases
as log L even up to L = 201. However, the histogram P(k) of the spanning
cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L,
indicating that for sufficiently large L the average will approach a finite
value: a fit of the 5D multiplicity data with a constant plus a simple linear
correction to scaling reproduces the data very well. Numerical simulations for
d>6 and for d=4 are also presented.Comment: 8 pages, 11 figures. Final version to appear on Physical Review
Glass glass transition and new dynamical singularity points in an analytically solvable p-spin glass like model
We introduce and analytically study a generalized p-spin glass like model
that captures some of the main features of attractive glasses, recently found
by Mode Coupling investigations, such as a glass/glass transition line and
dynamical singularity points characterized by a logarithmic time dependence of
the relaxation. The model also displays features not predicted by the Mode
Coupling scenario that could further describe the attractive glasses behavior,
such as aging effects with new dynamical singularity points ruled by
logarithmic laws or the presence of a glass spinodal line
Thermodynamics and statistical mechanics of frozen systems in inherent states
We discuss a Statistical Mechanics approach in the manner of Edwards to the
``inherent states'' (defined as the stable configurations in the potential
energy landscape) of glassy systems and granular materials. We show that at
stationarity the inherent states are distributed according a generalized Gibbs
measure obtained assuming the validity of the principle of maximum entropy,
under suitable constraints. In particular we consider three lattice models (a
diluted Spin Glass, a monodisperse hard-sphere system under gravity and a
hard-sphere binary mixture under gravity) undergoing a schematic ``tap
dynamics'', showing via Monte Carlo calculations that the time average of
macroscopic quantities over the tap dynamics and over such a generalized
distribution coincide. We also discuss about the general validity of this
approach to non thermal systems.Comment: 10 pages, 16 figure
Invaded cluster algorithm for a tricritical point in a diluted Potts model
The invaded cluster approach is extended to 2D Potts model with annealed
vacancies by using the random-cluster representation. Geometrical arguments are
used to propose the algorithm which converges to the tricritical point in the
two-dimensional parameter space spanned by temperature and the chemical
potential of vacancies. The tricritical point is identified as a simultaneous
onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of
"geometrical disorder cluster". The location of the tricritical point and the
concentration of vacancies for q = 1, 2, 3 are found to be in good agreement
with the best known results. Scaling properties of the percolating scaling
cluster and related critical exponents are also presented.Comment: 8 pages, 5 figure
Mode-coupling theory predictions for a limited valency attractive square-well model
Recently we have studied, using numerical simulations, a limited valency
model, i.e. an attractive square well model with a constraint on the maximum
number of bonded neighbors. Studying a large region of temperatures and
packing fractions , we have estimated the location of the liquid-gas
phase separation spinodal and the loci of dynamic arrest, where the system is
trapped in a disordered non-ergodic state. Two distinct arrest lines for the
system are present in the system: a {\it (repulsive) glass} line at high
packing fraction, and a {\it gel} line at low and . The former is
essentially vertical (-controlled), while the latter is rather horizontal
(-controlled) in the plane. We here complement the molecular
dynamics results with mode coupling theory calculations, using the numerical
structure factors as input. We find that the theory predicts a repulsive glass
line -- in satisfactory agreement with the simulation results -- and an
attractive glass line which appears to be unrelated to the gel line.Comment: 12 pages, 6 figures. To appear in J. Phys. Condens. Matter, special
issue: "Topics in Application of Scattering Methods for Investigation of
Structure and Dynamics of Soft Condensed Matter", Fiesole, November 200
Percolation transition and the onset of non exponential relaxation in fully frustrated models
We numerically study the dynamical properties of fully frustrated models in 2
and 3 dimensions. The results obtained support the hypothesis that the
percolation transition of the Kasteleyn-Fortuin clusters corresponds to the
onset of stretched exponential autocorrelation functions in systems without
disorder. This dynamical behavior may be due to the ``large scale'' effects of
frustration, present below the percolation threshold. Moreover these results
are consistent with the picture suggested by Campbell et al. in space of
configurations.Comment: 8 pages, 11 figures, revised versio
Non exponential relaxation in fully frustrated models
We study the dynamical properties of the fully frustrated Ising model. Due to
the absence of disorder the model, contrary to spin glass, does not exhibit any
Griffiths phase, which has been associated to non-exponential relaxation
dynamics. Nevertheless we find numerically that the model exhibits a stretched
exponential behavior below a temperature T_p corresponding to the percolation
transition of the Kasteleyn-Fortuin clusters. We have also found that the
critical behavior of this clusters for a fully frustrated q-state spin model at
the percolation threshold is strongly affected by frustration. In fact while in
absence of frustration the q=1 limit gives random percolation, in presence of
frustration the critical behavior is in the same universality class of the
ferromagnetic q=1/2-state Potts model.Comment: 7 pages, RevTeX, 11 figs, to appear on Physical Review
- …