Off equilibrium response function in the one dimensional random field Ising model

A thorough numerical investigation of the slow dynamics in the d=1 random field Ising model in the limit of an infinite ferromagnetic coupling is presented. Crossovers from the preasymptotic pure regime to the asymptotic Sinai regime are investigated for the average domain size, the autocorrelation function and staggered magnetization. By switching on an additional small random field at the time tw the linear off equilibrium response function is obtained, which displays as well the crossover from the nontrivial behavior of the d=1 pure Ising model to the asymptotic behavior where it vanishes identically.Comment: 12 pages, 10 figure

Thermal Operators in Ising Percolation

We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional Ising model, obtained by studying the percolation mapping of an Ising model with an arbitrary set of antiferromagnetic links. Such a representation relates the thermal operators to the topological properties of the Fortuin-Kasteleyn clusters of Ising percolation and is a powerful tool to get new exact relations on the topological structure of FK clusters of the Ising model defined on an arbitrary graph.Comment: 17 pages, 2 figures. Improved version. Major changes in the text and in the notations. A missing term added in the specific heat representatio

Comment on ``Two Time Scales and Violation of the Fluctuation-Dissipation Theorem in a Finite Dimensional Model for Structural Glasses''

In cond-mat/0002074 Ricci-Tersenghi et al. find two linear regimes in the fluctuation-dissipation relation between density-density correlations and associated responses of the Frustrated Ising Lattice Gas. Here we show that this result does not seem to correspond to the equilibrium quantities of the model, by measuring the overlap distribution P(q) of the density and comparing the FDR expected on the ground of the P(q) with the one measured in the off-equilibrium experiments.Comment: RevTeX, 1 page, 2 eps figures, Comment on F. Ricci-Tersenghi et al., Phys. Rev. Lett. 84, 4473 (2000

Sustainability charter for innovative cities and safe mobility. Case study: Sestri Levante

In order to make our cities more innovative and responsive, the paper reports a study aimed at defining a new sustainability tool, in the context of Agenda 2030, to be adopted in urban realities. It has to do with the 'Sustainability Charter', a city decision-making process, designed with researchers, local communities and companies. The research analyses the Sustainability Charter and develops a methodological approach aiming at the systemization of all sustainable actions related to different urban topics. In particular, indicators were identified to assess the sustainability of these topics, graphically represented by chart and defined as sustainability maps. In the paper, among the priority issues at urban level, sustainable mobility is explored. The current health emergency has highlighted all the problems related to urban mobility. This situation can represent an opportunity to improve, revise or update cities\u2019 governance tools. It is necessary to build safe soft mobility infrastructures, and to reorganize the existing ones -redesigning urban space-, by promoting a new culture of sustainable mobility. The Sustainable Urban Mobility Plan (SUMP), should integrate the Urban Sustainability Charter and all the underlying strategies to promote sustainable mobility

Mass media destabilizes the cultural homogeneous regime in Axelrod's model

An important feature of Axelrod's model for culture dissemination or social influence is the emergence of many multicultural absorbing states, despite the fact that the local rules that specify the agents interactions are explicitly designed to decrease the cultural differences between agents. Here we re-examine the problem of introducing an external, global interaction -- the mass media -- in the rules of Axelrod's model: in addition to their nearest-neighbors, each agent has a certain probability $p$ to interact with a virtual neighbor whose cultural features are fixed from the outset. Most surprisingly, this apparently homogenizing effect actually increases the cultural diversity of the population. We show that, contrary to previous claims in the literature, even a vanishingly small value of $p$ is sufficient to destabilize the homogeneous regime for very large lattice sizes

Metastable states in the Blume-Emery-Griffiths spin glass model

We study the Blume-Emery-Griffiths spin glass model in presence of an attractive coupling between real replicas, and evaluate the effective potential as a function of the density overlap. We find that there is a region, above the first order transition of the model, where metastable states with a large density overlap exist. The line where these metastable states appear should correspond to a purely dynamical transition, with a breaking of ergodicity. Differently from what happens in p-spin glasses, in this model the dynamical transition would not be the precursor of a 1-step RSB transition, but (probably) of a full RSB transition.Comment: RevTeX, 4 pages, 2 fig

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

Ultra-high energy cosmic rays from Quark Novae

We explore acceleration of ions in the Quark Nova (QN) scenario, where a neutron star experiences an explosive phase transition into a quark star (born in the propeller regime). In this picture, two cosmic ray components are isolated: one related to the randomized pulsar wind and the other to the propelled wind, both boosted by the ultra-relativistic Quark Nova shock. The latter component acquires energies $10^{15} {\rm eV}<E<10^{18} {\rm eV}$ while the former, boosted pulsar wind, achieves ultra-high energies $E> 10^{18.6}$ eV. The composition is dominated by ions present in the pulsar wind in the energy range above $10^{18.6}$ eV, while at energies below $10^{18}$ eV the propelled ejecta, consisting of the fall-back neutron star crust material from the explosion, is the dominant one. Added to these two components, the propeller injects relativistic particles with Lorentz factors $\Gamma_{\rm prop.} \sim 1-1000$, later to be accelerated by galactic supernova shocks. The QN model appears to be able to account for the extragalactic cosmic rays above the ankle and to contribute a few percent of the galactic cosmic rays below the ankle. We predict few hundred ultra-high energy cosmic ray events above $10^{19}$ eV for the Pierre Auger detector per distant QN, while some thousands are predicted for the proposed EUSO and OWL detectors.Comment: 20 pages, 1 figure. Major revisions in the text. Accepted for publication in the Astrophysical Journa