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 $r$ 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 $\rho(r)$. The model is analytically solvable in $d=2$ 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 $\beta$ 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

Invaded Cluster Dynamics for Frustrated Models

The Invaded Cluster (IC) dynamics introduced by Machta et al. [Phys. Rev. Lett. 75 2792 (1995)] is extended to the fully frustrated Ising model on a square lattice. The properties of the dynamics which exhibits numerical evidence of self-organized criticality are studied. The fluctuations in the IC dynamics are shown to be intrinsic of the algorithm and the fluctuation-dissipation theorem is no more valid. The relaxation time is found very short and does not present critical size dependence.Comment: notes and refernences added, some minor changes in text and fig.3,5,7 16 pages, Latex, 8 EPS figures, submitted to Phys. Rev.