61 research outputs found
The Blume-Emery-Griffiths Spin Glass Model
No full textWe introduced and investigated the Blume-Emery-Griffiths Spin Glass Model
Kovacs effect in facilitated spin models of strong and fragile glasses
No full textWe investigate the Kovacs (or crossover) effect in facilitated f-spin models of glassy dynamics. Although the Kovacs hump shows a behavior qualitatively similar for all cases we have examined (irrespective of the facilitation parameter f and the spatial dimension d), we find that the dependence of the Kovacs peak time on the temperature of the second quench allows to distinguish among different microscopic mechanisms responsible for the glassy relaxation (e.g. cooperative vs defect diffusion). We also analyze the inherent structure dynamics underlying the Kovacs protocol, and find that the class of facilitated spin models with d>1 and f>1 shows features resembling those obtained recently in a realistic model of fragile glass forming liquid. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2004
Equilibrium properties of the Ising frustrated lattice gas
No full textReplica approach investigation of the Ising frustrated spin glass
Microscopic models of mode-coupling theory: The F12 scenario
No full textWe provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the F12
schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation.
Depending on the facilitation strength, one observes two distinct dynamical glass transition lines—continuous and discontinuous—merging at a dynamical tricritical-like point with critical decay
exponents consistently related by MCT predictions. The mechanisms of dynamical arrest can be naturally interpreted in geometrical terms: the discontinuous and continuous transitions correspond to
bootstrap and standard percolation processes, in which the incipient spanning cluster of frozen spins
forms either a compact or a fractal structure, respectively. Our cooperative dynamical facilitation picture of glassy behavior is complementary to the one based on disordered systems and can account for higher-order singularity scenarios in the absence of a finite temperature thermodynamic glass
transition. We briefly comment on the relevance of our results to finite spatial dimensions and to the F13 schematic model
Two Time Scales and Violation of the Fluctuation-Dissipation Theorem in a Finite Dimensional Model for Structural Glasses
No full textWe study the breakdown of fluctuation-dissipation relations between time-dependent density-density correlations and associated responses following a quench in the chemical potential in the frustrated Ising lattice gas. The corresponding slow dynamics is characterized by two well-separated time scales characterized by a constant value of the fluctuation-dissipation ratio. This result is particularly relevant since activated processes dominate the long-time dynamics of the system
Aging dynamics and density relaxation in kinetic lattice gases under gravity
No full textWe present an analytical approach to the out-of-equilibrium dynamics of a class of kinetic lattice gases under gravity. The location of the jamming transition, the critical exponents, and the scaling functions characterizing the relaxation processes are determined. In particular, we nd that logarithmic compaction and simple aging are intimately related to the Vogel-Fulcher law, while power law compaction and super-aging behavior occur in the presence of a power law diffusion
Dynamics of the frustrated Ising lattice gas
No full textThe dynamical properties of a three-dimensional model glass, the frustrated Ising lattice gas (FILG), are studied by Monte Carlo simulations. We present results of compression experiments, where the chemical potential is either slowly or abruptly changed, as well as simulations at constant density. One time quantities like density and two time quantities like correlations, responses, and mean square displacements are measured, and the departure from equilibrium clearly characterized. The aging scenario, particularly in the case of density autocorrelations, is reminiscent of spin glass phenomenology with violations of the fluctuation-dissipation theorem, typical of systems with one replica symmetry breaking. The FILG, as a valid on-lattice model of structural glasses, can be described with tools developed in spin glass theory and, being a finite-dimensional model, can open the way for a systematic study of activated processes in glasses
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No full text[No abstract available
Maximal Diversity and Zipf's Law
No full textZipf's law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipf's law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps's law is discussed. As an example, we show that our analytical results compare very well with linguistics and population datasets
Dynamic Facilitation Picture of a Higher-Order Glass Singularity
No full textWe show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the facilitation strength, they yield either a discontinuous glass transition or a continuous one, with no underlying thermodynamic singularity. Similar results are obtained for facilitated spin models on a diluted Bethe lattice. The mechanism of dynamical arrest in these systems can be interpreted in terms of bootstrap and standard percolation and corresponds to a crossover from a compact to a fractal structure of the incipient spanning cluster of frozen spins. Theoretical and numerical simulation results are fully consistent with MCT predictions
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