Glassy states in lattice models with many coexisting crystalline phases

We study the emergence of glassy states after a sudden cooling in lattice models with short range interactions and without any a priori quenched disorder. The glassy state emerges whenever the equilibrium model possesses a sufficient number of coexisting crystalline phases at low temperatures, provided the thermodynamic limit be taken before the infinite time limit. This result is obtained through simulations of the time relaxation of the standard Potts model and some exclusion models equipped with a local stochastic dynamics on a square lattice.Comment: 12 pages, 4 figure

Glassy behaviour in short range lattice models without quenched disorder

We investigate the quenching process in lattice systems with short range interaction and several crystalline states as ground states. We consider in particular the following systems on square lattice: - hard particle (exclusion) model; - q states planar Potts model. The system is initially in a homogeneous disordered phase and relaxes toward a new equilibrium state as soon as the temperature is rapidly lowered. The time evolution can be described numerically by a stochastic process such as the Metropolis algorithm. The number of pure, equivalent, ground states is q for the Potts model and r for the hard particle model, and it is known that for r or q larger or equal to d+1, the final equilibrium state may be polycrystalline, i.e. not made of a uniform phase. We find that in addition n_g and q_g exist such that for r > r_g, or q > q_g the system evolves toward a glassy state, i.e. a state in which the ratio of the interaction energy among the different crystalline phases to the total energy of the system never vanishes; moreover we find indications that r_g=q_g. We infer that q=q_g (and r=r_g) corresponds to the crossing from second order to discontinuous transition in the phase diagram of the system.Comment: 10 pages, 3 figure

Lattice models of disorder with order

This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are not subject to constrained evolution rules. After a short review of some of these models, the paper discusses how two particularly simple kinds of models, the Potts model and the exclusion models, evolve after a quench at low temperature to glassy states rather than to crystalline states

Dynamical heterogeneities as fingerprints of a backbone structure in Potts models

We investigate slow non-equilibrium dynamical processes in two-dimensional $q$--state Potts model with both ferromagnetic and $\pm J$ couplings. Dynamical properties are characterized by means of the mean-flipping time distribution. This quantity is known for clearly unveiling dynamical heterogeneities. Using a two-times protocol we characterize the different time scales observed and relate them to growth processes occurring in the system. In particular we target the possible relation between the different time scales and the spatial heterogeneities originated in the ground state topology, which are associated to the presence of a backbone structure. We perform numerical simulations using an approach based on graphics processing units (GPUs) which permits to reach large system sizes. We present evidence supporting both the idea of a growing process in the preasymptotic regime of the glassy phases and the existence of a backbone structure behind this processes.Comment: 9 pages, 7 figures, Accepted for publication in PR

Inference of hidden structures in complex physical systems by multi-scale clustering

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work

Topics in coarsening phenomena

These lecture notes give a very short introduction to coarsening phenomena and summarize some recent results in the field. They focus on three aspects: the super-universality hypothesis, the geometry of growing structures, and coarsening in the spiral kinetically constrained model.Comment: Lecture notes. Fundamental Problems in Statistical Physics XII, Leuven, Aug 30 - Sept 12, 200

Some recent developments in models with absorbing states

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe some of the results obtained in the context of synchronization of chaotic dynamical systems. Moreover, we discuss the relation of the synchronization transition with some interfacial models.Comment: 8 pages, Brazilian J. of Physics (in press

Following Gibbs States Adiabatically - The Energy Landscape of Mean Field Glassy Systems

We introduce a generalization of the cavity, or Bethe-Peierls, method that allows to follow Gibbs states when an external parameter, e.g. the temperature, is adiabatically changed. This allows to obtain new quantitative results on the static and dynamic behavior of mean field disordered systems such as models of glassy and amorphous materials or random constraint satisfaction problems. As a first application, we discuss the residual energy after a very slow annealing, the behavior of out-of-equilibrium states, and demonstrate the presence of temperature chaos in equilibrium. We also explore the energy landscape, and identify a new transition from an computationally easier canyons-dominated region to a harder valleys-dominated one.Comment: 6 pages, 7 figure