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

Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet

We introduce a lattice model for a classical doped two dimensional antiferromagnet which has no quenched disorder, yet displays slow dynamics similar to those observed in supercooled liquids. We calculate two-time spatial and spin correlations via Monte Carlo simulations and find that for sufficiently low temperatures, there is anomalous diffusion and stretched-exponential relaxation of spin correlations. The relaxation times associated with spin correlations and diffusion both diverge at low temperatures in a sub-Arrhenius fashion if the fit is done over a large temperature-window or an Arrhenius fashion if only low temperatures are considered. We find evidence of spatially heterogeneous dynamics, in which vacancies created by changes in occupation facilitate spin flips on neighbouring sites. We find violations of the Stokes-Einstein relation and Debye-Stokes-Einstein relation and show that the probability distributions of local spatial correlations indicate fast and slow populations of sites, and local spin correlations indicate a wide distribution of relaxation times, similar to observ ations in other glassy systems with and without quenched disorder.Comment: 12 pages, 17 figures, corrected erroneous figure, and improved quality of manuscript, updated reference

Critical Droplets and Phase Transitions in Two Dimensions

In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing a bond probability p_B<1, the corresponding site-bond clusters keep on percolating at T_c and the exponents do not change, until p_B=p_CK=1-exp(-2J/kT): for this special expression of the bond weight the critical percolation exponents switch to the 2D Ising universality class. We show here that the result is valid for a wide class of bidimensional models with a continuous magnetization transition: there is a critical bond probability p_c such that, for any p_B>=p_c, the onset of percolation of the site-bond clusters coincides with the critical point of the thermal transition. The percolation exponents are the same for p_c<p_B<=1 but, for p_B=p_c, they suddenly change to the thermal exponents, so that the corresponding clusters are critical droplets of the phase transition. Our result is based on Monte Carlo simulations of various systems near criticality.Comment: Final version for publication, minor changes, figures adde

The jamming transition of Granular Media

We briefly review the basics ideas and results of a recently proposed statistical mechanical approach to granular materials. Using lattice models from standard Statistical Mechanics and results from a mean field replica approach and Monte Carlo simulations we find a jamming transition in granular media closely related to the glass transition in super-cooled liquids. These models reproduce the logarithmic relaxation in granular compaction and reversible-irreversible lines, in agreement with experimental data. The models also exhibit aging effects and breakdown of the usual fluctuation dissipation relation. It is shown that the glass transition may be responsible for the logarithmic relaxation and may be related to the cooperative effects underlying many phenomena of granular materials such as the Reynolds transition.Comment: 18 pages with 6 postscript figures. to appear in J.Phys: Cond. Ma

Percolation and number of phases in the 2D Ising model

We reconsider the percolation approach of Russo, Aizenman and Higuchi for showing that there exist only two phases in the Ising model on the square lattice. We give a fairly short alternative proof which is only based on FKG monotonicity and avoids the use of GKS-type inequalities originally needed for some background results. Our proof extends to the Ising model on other planar lattices such as the triangular and honeycomb lattice. We can also treat the Ising antiferromagnet in an external field and the hard-core lattice gas model on $Z^2$.Comment: 22 pages. Further details on extensions. To appear in J.Math.Phys., special issue on `Probabilistic Methods in Statistical Physics', March 200

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.

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

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

Fuzzy formal concept analysis

CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORFormal Context Analysis is a mathematical theory that enables us to find concepts from a given set of objects, a set of attributes and a relation on them. There is a hierarchy of such concepts, from which a complete lattice can be made. In this paper we p831192205CNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIORCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOCAPES - COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL E NÍVEL SUPERIOR306546/2017-5308524/2014-437th Conference of the North-American-Fuzzy-Information-Processing-Society (NAFIPS

Correlated percolation and the correlated resistor network

We present some exact results on percolation properties of the Ising model, when the range of the percolating bonds is larger than nearest-neighbors. We show that for a percolation range to next-nearest neighbors the percolation threshold Tp is still equal to the Ising critical temperature Tc, and present the phase diagram for this type of percolation. In addition, we present Monte Carlo calculations of the finite size behavior of the correlated resistor network defined on the Ising model. The thermal exponent t of the conductivity that follows from it is found to be t = 0.2000 +- 0.0007. We observe no corrections to scaling in its finite size behavior.Comment: 16 pages, REVTeX, 6 figures include