249 research outputs found
Precursor phenomena in frustrated systems
To understand the origin of the dynamical transition, between high
temperature exponential relaxation and low temperature nonexponential
relaxation, that occurs well above the static transition in glassy systems, a
frustrated spin model, with and without disorder, is considered. The model has
two phase transitions, the lower being a standard spin glass transition (in
presence of disorder) or fully frustrated Ising (in absence of disorder), and
the higher being a Potts transition. Monte Carlo results clarify that in the
model with (or without) disorder the precursor phenomena are related to the
Griffiths (or Potts) transition. The Griffiths transition is a vanishing
transition which occurs above the Potts transition and is present only when
disorder is present, while the Potts transition which signals the effect due to
frustration is always present. These results suggest that precursor phenomena
in frustrated systems are due either to disorder and/or to frustration, giving
a consistent interpretation also for the limiting cases of Ising spin glass and
of Ising fully frustrated model, where also the Potts transition is vanishing.
This interpretation could play a relevant role in glassy systems beyond the
spin systems case.Comment: Completely rewritten. New data. New result
Lamellar order, microphase structures and glassy phase in a field theoretic model for charged colloids
In this paper we present a detailed analytical study of the phase diagram and
of the structural properties of a field theoretic model with a short-range
attraction and a competing long-range screened repulsion. We provide a full
derivation and expanded discussion and digression on results previously
reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702
(2006). The model contains the essential features of the effective interaction
potential among charged colloids in polymeric solutions. We employ the
self-consistent Hartree approximation and a replica approach, and we show that
varying the parameters of the repulsive potential and the temperature yields a
phase coexistence, a lamellar and a glassy phase. Our results suggest that the
cluster phase observed in charged colloids might be the signature of an
underlying equilibrium lamellar phase, hidden on experimental time scales, and
emphasize that the formation of microphase structures may play a prominent role
in the process of colloidal gelation.Comment: 16 pages, 7 figure
Scaling and universality in glass transition
Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are
within those systems known to exhibit a discontinuous dynamical transition with
a two step relaxation. We consider a general scaling approach, within mean
field theory, for such systems by considering the behavior of the density
correlator and the dynamical susceptibility -^2. Focusing
on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe
lattice, we extend a cluster approach that was previously developed for
continuous glass transitions by Arenzon et al (Phys. Rev. E 90, 020301(R)
(2014)) to describe the decay to the plateau, and consider a damage spreading
mechanism to describe the departure from the plateau. We predict scaling laws,
which relate dynamical exponents to the static exponents of mean field
bootstrap percolation. The dynamical behavior and the scaling laws for both
density correlator and dynamical susceptibility coincide with those predicted
by MCT. These results explain the origin of scaling laws and the universal
behavior associated with the glass transition in mean field, which is
characterized by the divergence of the static length of the bootstrap
percolation model with an upper critical dimension d_c=8.Comment: 16 pages, 9 figure
Disordered jammed packings of frictionless spheres
At low volume fraction, disordered arrangements of frictionless spheres are
found in un--jammed states unable to support applied stresses, while at high
volume fraction they are found in jammed states with mechanical strength. Here
we show, focusing on the hard sphere zero pressure limit, that the transition
between un-jammed and jammed states does not occur at a single value of the
volume fraction, but in a whole volume fraction range. This result is obtained
via the direct numerical construction of disordered jammed states with a volume
fraction varying between two limits, and . We identify these
limits with the random loose packing volume fraction \rl and the random close
packing volume fraction \rc of frictionless spheres, respectively
Segregation in hard spheres mixtures under gravity. An extension of Edwards approach with two thermodynamical parameters
We study segregation patterns in a hard sphere binary model under gravity
subject to sequences of taps. We discuss the appearance of the ``Brazil nut''
effect (where large particles move up) and the ``reverse Brazil nut'' effects
in the stationary states reached by ``tap'' dynamics. In particular, we show
that the stationary state depends only on two thermodynamical quantities: the
gravitational energy of the first and of the second species and not on the
sample history. To describe the properties of the system, we generalize
Edwards' approach by introducing a canonical distribution characterized by two
configurational temperatures, conjugate to the energies of the two species.
This is supported by Monte Carlo calculations showing that the average of
several quantities over the tap dynamics and over such distribution coincide.
The segregation problem can then be understood as an equilibrium statistical
mechanics problem with two control parameters.Comment: 7 pages, 4 figure
Crossover properties from random percolation to frustrated percolation
We investigate the crossover properties of the frustrated percolation model
on a two-dimensional square lattice, with asymmetric distribution of
ferromagnetic and antiferromagnetic interactions. We determine the critical
exponents nu, gamma and beta of the percolation transition of the model, for
various values of the density of antiferromagnetic interactions pi in the range
0<pi<0.5. Our data are consistent with the existence of a crossover from random
percolation behavior for pi=0, to frustrated percolation behavior,
characterized by the critical exponents of the ferromagnetic 1/2-state Potts
model, as soon as pi>0.Comment: 5 pages, 7 figs, RevTe
Spatial correlations of elementary relaxation events in glass-forming liquids
The dynamical facilitation scenario, by which localized relaxation events
promote nearby relaxation events in an avalanching process, has been suggested
as the key mechanism connecting the microscopic and the macroscopic dynamics of
structural glasses. Here we investigate the statistical features of this
process via the numerical simulation of a model structural glass. First we show
that the relaxation dynamics of the system occurs through particle jumps that
are irreversible, and that cannot be decomposed in smaller irreversible events.
Then we show that each jump does actually trigger an avalanche. The
characteristic of this avalanche change on cooling, suggesting that the
relaxation dynamics crossovers from a noise dominated regime where jumps do not
trigger other relaxation events, to a regime dominated by the facilitation
process, where a jump trigger more relaxation events.Comment: 8 pages, 6 figure
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