Off equilibrium dynamics of the Frustrated Ising Lattice Gas

We study by means of Monte Carlo simulations the off equilibrium properties of a model glass, the Frustrated Ising Lattice Gas (FILG) in three dimensions. We have computed typical two times quantities, like density-density autocorrelations and the autocorrelation of internal degrees of freedom. We find an aging scenario particularly interesting in the case of the density autocorrelations in real space which is very reminiscent of spin glass phenomenology. While this model captures the essential features of structural glass dynamics, its analogy with spin glasses may bring the possibility of its complete description using the tools developed in spin glass theory.Comment: Phys. Rev. E (Rapid Communication), 1999 (probably May

Kosterlitz-Thouless and Potts transitions in a generalized XY model

We present extensive numerical simulations of a generalized XY model with nematic-like terms recently proposed by Poderoso {\it et al} [PRL 106(2011)067202]. Using finite size scaling and focusing on the $q=3$ case, we locate the transitions between the paramagnetic (P), the nematic-like (N) and the ferromagnetic (F) phases. The results are compared with the recently derived lower bounds for the P-N and P-F transitions. While the P-N transition is found to be very close to the lower bound, the P-F transition occurs significantly above the bound. Finally, the transition between the nematic-like and the ferromagnetic phases is found to belong to the 3-states Potts universality class.Comment: Extended and updated version of arXiv:1207.3447v

Competing nematic interactions in a generalized XY model in two and three dimensions

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of $2\pi/q$ between neighboring spins. We focus here on the $q=8$ case (while presenting new results for other values of $q$ as well) whose phase diagram is much richer than the well known $q=2$ case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in $q=2$, but also infinite order transitions involving intermediate, competition driven phases absent for $q=2$ and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a suficient condition for it to be of BKT type.Comment: 13 pages, 16 figure

Heterogeneities in systems with quenched disorder

We study the strong role played by structural (quenched) heterogeneities on static and dynamic properties of the Frustrated Ising Lattice Gas in two dimensions, already in the liquid phase. Differently from the dynamical heterogeneities observed in other glass models in this case they may have infinite lifetime and be spatially pinned by the quenched disorder. We consider a measure of local frustration, show how it induces the appearance of spatial heterogeneities and how this reflects in the observed behavior of equilibrium density distributions and dynamic correlation functions.Comment: 8 page

A branching random-walk model of disease outbreaks and the percolation backbone

The size and shape of the region affected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents diffuse on a regular lattice and the disease may be transmitted when an infected and a susceptible agents are nearest neighbors. We study the geometric properties of both the connected cluster of sites visited by infected agents (outbreak cluster) and the set of clusters with sites that have not been visited. By changing the density of agents, our results show that there is a mixed-order (hybrid) transition where the region affected by the disease is finite in one phase but percolates through the system beyond the threshold. Moreover, the outbreak cluster seems to have the same exponents of the backbone of the critical cluster of the ordinary percolation while the clusters with unvisited sites have a size distribution with a Fisher exponent $\tau<2$.Comment: 7 pages, 7 figure

Two time scales and FDT violation in a Finite Dimensional Model for Structural Glasses

We study the breakdown of fluctuation-dissipation relations between time dependent density-density correlations and associated responses following a quench in chemical potential in the Frustrated Ising Lattice Gas. The corresponding slow dynamics is characterized by two well separated time scales which are characterized by a constant value of the fluctuation-dissipation ratio. This result is particularly relevant taking into account that activated processes dominate the long time dynamics of the system.Comment: 4 pages, 3 figs, Phys. Rev. Lett. (in press

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

Energy-lowering and constant-energy spin flips: Emergence of the percolating cluster in the kinetic Ising model

After a sudden quench from the disordered high-temperature T0→∞ phase to a final temperature well below the critical point TF≪Tc, the nonconserved order parameter dynamics of the two-dimensional ferromagnetic Ising model on a square lattice initially approaches the critical percolation state before entering the coarsening regime. This approach involves two timescales associated with the first appearance (at time tp1>0) and stabilization (at time tp>tp1) of a giant percolation cluster, as previously reported. However, the microscopic mechanisms that control such timescales are not yet fully understood. In this paper, to study their role on each time regime after the quench (TF=0), we distinguish between spin flips that decrease the total energy of the system from those that keep it constant, the latter being parametrized by the probability p. We show that observables such as the cluster size heterogeneity H(t,p) and the typical domain size ℓ(t,p) have no dependence on p in the first time regime up to tp1. Furthermore, when energy-decreasing flips are forbidden while allowing constant-energy flips, the kinetics is essentially frozen after the quench and there is no percolation event whatsoever. Taken together, these results indicate that the emergence of the first percolating cluster at tp1 is completely driven by energy decreasing flips. However, the time for stabilizing a percolating cluster is controlled by the acceptance probability of constant-energy flips: tp(p)∼p−1 for p≪1 (at p=0, the dynamics gets stuck in a metastable state). These flips are also the relevant ones in the later coarsening regime where dynamical scaling takes place. Because the phenomenology on the approach to the percolation point seems to be shared by many 2D systems with a nonconserved order parameter dynamics (and certain cases of conserved ones as well), our results may suggest a simple and effective way to set, through the dynamics itself, tp1 and tp in such systems