1,376 research outputs found
Phase Transitions in Granular Packings
We describe the contact network of granular packings by a frustrated lattice
gas that contains steric frustration as essential ingredient. Two transitions
are identified, a spin glass transition at the onset of Reynolds dilatancy and
at lower densities a percolation transition. We describe the correlation
functions that give rise to the singularities and propose some dynamical
experiments
Dynamics and thermodynamics of the spherical frustrated Blume-Emery-Griffiths model
We introduce a spherical version of the frustrated Blume-Emery-Griffiths
model and solve exactly the statics and the Langevin dynamics for zero
particle-particle coupling (K=0). In this case the model exhibits an
equilibrium transition from a disordered to a spin glass phase which is always
continuous for nonzero temperature. The same phase diagram results from the
study of the dynamics. Furthermore, we notice the existence of a nonequilibrium
time regime in a region of the disordered phase, characterized by aging as
occurs in the spin glass phase. Due to a finite equilibration time, the system
displays in this region the pattern of interrupted aging.Comment: 19 pages, 8 figure
A Geometrical Interpretation of Hyperscaling Breaking in the Ising Model
In random percolation one finds that the mean field regime above the upper
critical dimension can simply be explained through the coexistence of infinite
percolating clusters at the critical point. Because of the mapping between
percolation and critical behaviour in the Ising model, one might check whether
the breakdown of hyperscaling in the Ising model can also be intepreted as due
to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the
critical temperature T_c. Preliminary results suggest that the scenario is much
more involved than expected due to the fact that the percolation variables
behave differently on the two sides of T_c.Comment: Lattice2002(spin
Static and dynamic heterogeneities in irreversible gels and colloidal gelation
We compare the slow dynamics of irreversible gels, colloidal gels, glasses
and spin glasses by analyzing the behavior of the so called non-linear
dynamical susceptibility, a quantity usually introduced to quantitatively
characterize the dynamical heterogeneities. In glasses this quantity typically
grows with the time, reaches a maximum and then decreases at large time, due to
the transient nature of dynamical heterogeneities and to the absence of a
diverging static correlation length. We have recently shown that in
irreversible gels the dynamical susceptibility is instead an increasing
function of the time, as in the case of spin glasses, and tends asymptotically
to the mean cluster size. On the basis of molecular dynamics simulations, we
here show that in colloidal gelation where clusters are not permanent, at very
low temperature and volume fractions, i.e. when the lifetime of the bonds is
much larger than the structural relaxation time, the non-linear susceptibility
has a behavior similar to the one of the irreversible gel, followed, at higher
volume fractions, by a crossover towards the behavior of glass forming liquids.Comment: 9 pages, 3 figure
Phase coexistence and relaxation of the spherical frustrated Blume-Emery-Griffiths model with attractive particles coupling
We study the equilibrium and dynamical properties of a spherical version of
the frustrated Blume-Emery-Griffiths model at mean field level for attractive
particle-particle coupling (K>0). Beyond a second order transition line from a
paramagnetic to a (replica symmetric) spin glass phase, the density-temperature
phase diagram is characterized by a tricritical point from which,
interestingly, a first order transition line starts with coexistence of the two
phases. In the Langevin dynamics the paramagnetic/spin glass discontinuous
transition line is found to be dependent on the initial density; close to this
line, on the paramagnetic side, the correlation-response plot displays
interrupted aging.Comment: to be published on Europhysics Letter
Random walk, cluster growth, and the morphology of urban conglomerations
We propose a new model of cluster growth according to which the probability
that a new unit is placed in a point at a distance from the city center is
a Gaussian with mean equal to the cluster radius and variance proportional to
the mean, modulated by the local density . The model is analytically
solvable in dimensions, where the density profile varies as a
complementary error function. The model reproduces experimental observations
relative to the morphology of cities, determined via an original analysis of
digital maps with a very high spatial resolution, and helps understanding the
emergence of vehicular traffic.Comment: Physica A. To appea
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
Site Percolation and Phase Transitions in Two Dimensions
The properties of the pure-site clusters of spin models, i.e. the clusters
which are obtained by joining nearest-neighbour spins of the same sign, are
here investigated. In the Ising model in two dimensions it is known that such
clusters undergo a percolation transition exactly at the critical point. We
show that this result is valid for a wide class of bidimensional systems
undergoing a continuous magnetization transition. We provide numerical evidence
for discrete as well as for continuous spin models, including SU(N) lattice
gauge theories. The critical percolation exponents do not coincide with the
ones of the thermal transition, but they are the same for models belonging to
the same universality class.Comment: 8 pages, 6 figures, 2 tables. Numerical part developed; figures,
references and comments adde
Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model
The evolution of the structure factor is studied during the phase-ordering
dynamics of the kinetic Ising model with conserved order parameter. A
preasymptotic multiscaling regime is found as in the solution of the
Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is
always approached through a crossover from multiscaling to standard scaling,
independently from the nature of the microscopic dynamics.Comment: 11 pages, 3 figures, to be published in Europhys. Let
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