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Alessandro Pluchino

Publications and source records attributed to Alessandro Pluchino.

48 records · Page 3Linked to original sources
arXiv2006

Compromise and Synchronization in Opinion Dynamics

We discuss two models of opinion dynamics. First wepresent a brief review of the Hegselmann and Krause (HK) compromise model in two dimensions, showing that it is possible to simulate the dynamics in the limit of an infinite number of agents by solving numerically a rate equation for a continuum distribution of opinions. Then, we discuss the Opinion Changing Rate (OCR) model, which allows to study under which conditions a group of agents with a different natural tendency (rate) to change opinion can find the agreement. In the context of the this model, consensus is viewed as a synchronization process.

physics.soc-ph↗
arXiv2006

Effective spin-glass Hamiltonian for the anomalous dynamics of the HMF model

We discuss an effective spin-glass Hamiltonian which can be used to study the glassy-like dynamics observed in the metastable states of the Hamiltonian Mean Field (HMF) model. By means of the Replica formalism, we were able to find a self-consistent equation for the glassy order parameter which reproduces, in a restricted energy region below the phase transition, the microcanonical simulations for the polarization order parameter recently introducted in the HMF model.

cond-mat.stat-mech↗
arXiv2005

Metastability in the Hamiltonian Mean Field model and Kuramoto model

We briefly discuss the state of the art on the anomalous dynamics of the Hamiltonian Mean Field model. We stress the important role of the initial conditions for understanding the microscopic nature of the intriguing metastable quasi stationary states observed in the model and the connections to Tsallis statistics and glassy dynamics. We also present new results on the existence of metastable states in the Kuramoto model and discuss the similarities with those found in the HMF model. The existence of metastability seem to be quite a common phenomenon in fully coupled systems, whose origin could be also interpreted as a dynamical mechanism preventing or hindering sinchronization.

cond-mat.stat-mech↗
arXiv2005

Olami-Feder-Christensen Model on different Networks

We investigate numerically the Self Organized Criticality (SOC) properties of the dissipative Olami-Feder-Christensen model on small-world and scale-free networks. We find that the small-world OFC model exhibits self-organized criticality. Indeed, in this case we observe power law behavior of earthquakes size distribution with finite size scaling for the cut-off region. In the scale-free OFC model, instead, the strength of disorder hinders synchronization and does not allow to reach a critical state.

cond-mat.stat-mech↗
arXiv2005

Nonextensive Thermodynamics and Glassy behaviour in Hamiltonian systems

An instructive and apparently simple model of fully-coupled rotators, the so-called Hamiltonian Mean Field (HMF) model, together with a generalized version with variable interaction range, have revealed a very complex out-of-equilibrium dynamics which can be considered paradigmatic for nonextensive systems. In this short paper we illustrate the interesting anomalous pre-equilibrium dynamics, focusing on the novel connections to the generalized nonextensive thermostatistics and the recent links to glassy systems.

cond-mat.stat-mech↗
arXiv2005

Vector Opinion Dynamics in a Bounded Confidence Consensus Model

We study the continuum opinion dynamics of the compromise model of Krause and Hegselmann for a community of mutually interacting agents, by solving numerically a rate equation. The opinions are here represented by bidimensional vectors with real-valued components. We study the situation starting from a uniform probability distribution for the opinion configuration and for different shapes of the confidence range. In all cases, we find that the thresholds for consensus and cluster merging either coincide with their one-dimensional counterparts, or are very close to them. The symmetry of the final opinion configuration, when more clusters survive, is determined by the shape of the opinion space. If the latter is a square, which is the case we consider, the clusters in general occupy the sites of a square lattice, although we sometimes observe interesting deviations from this general pattern, especially near the center of the opinion space.

physics.soc-ph↗
arXiv2004

Dynamics and Thermodynamics of a model with long-range interactions

The dynamics and the thermodynamics of particles/spins interacting via long-range forces display several unusual features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions represents a paradigmatic example of this class of systems. The equilibrium properties of the model can be derived analytically in the canonical ensemble: in particular the model shows a second order phase transition from a ferromagnetic to a paramagnetic phase. Strong anomalies are observed in the process of relaxation towards equilibrium for a particular class of out-of-equilibrium initial conditions. In fact the numerical simulations show the presence of quasi-stationary state (QSS), i.e. metastable states which become stable if the thermodynamic limit is taken before the infinite time limit. The QSS differ strongly from Boltzmann-Gibbs equilibrium states: they exhibit negative specific heat, vanishing Lyapunov exponents and weak mixing, non-Gaussian velocity distributions and anomalous diffusion, slowly-decaying correlations and aging. Such a scenario provides strong hints for the possible application of Tsallis generalized thermostatistics. The QSS have been recently interpreted as a spin-glass phase of the model. This link indicates another promising line of research, which is not alternative to the previous one.

cond-mat.stat-mech↗
arXiv2004

A Monte Carlo Investigation of the Hamiltonian Mean Field Model

We present a Monte Carlo numerical investigation of the Hamiltonian Mean Field (HMF) model. We begin by discussing canonical Metropolis Monte Carlo calculations, in order to check the caloric curve of the HMF model and study finite size effects. In the second part of the paper, we present numerical simulations obtained by means of a modified Monte Carlo procedure with the aim to test the stability of those states at minimum temperature and zero magnetization (homogeneous Quasi Stationary States) which exist in the condensed phase of the model just below the critical point. For energy densities smaller than the limiting value $U\sim 0.68$, we find that these states are unstable, confirming a recent result on the Vlasov stability analysis applied to the HMF model.

cond-mat.stat-mech↗
arXiv2003

Glassy dynamics in the HMF model

We discuss the glassy dynamics recently found in the meta-equilibrium quasi stationary states (QSS) of the HMF model. The relevance of the initial conditions and the connection with Tsallis nonextensive thermostatistics is also addressed.

cond-mat.stat-mech↗
arXiv2003

Glassy phase in the Hamiltonian Mean Field model

We study the relaxation dynamics of a Hamiltonian system of N fully-coupled XY spins. The thermodynamics of the system predicts a ferromagnetic and a paramagnetic phase. Starting from out-of-equilibrium initial conditions, the dynamics at constant energy drives the system into quasi-stationary states (QSS) characterized by dynamical frustration. We introduce the spin polarization as a new order parameter which allows to interpret the dynamically generated QSS regime as a glassy phase of the model.

cond-mat.stat-mech↗
arXiv2003

Metastable states, anomalous distributions and correlations in the HMF model

We study the microscopic dynamics of the metastable Quasi-Stationary States (QSS) in the Hamiltonian Mean Field (HMF) model, a Hamiltonian system of N classical inertial spins with infinite-range interactions which shows a second order phase transition. In order to understand the origin of metastability, which appears in an energy region below the critical point, we consider two different classes of out-of-equilibrium initial conditions, both leading to QSS, and having respectively initial magnetization equal to one (M1 IC) and equal to zero (M0 IC). We compare the corresponding $μ$-space, the resulting velocity pdfs and correlations, and the eventual aging features of the microscopic dynamics. In both cases the model exhibits non-gaussian pdfs, though anomalous correlations are present only when the system is started with an initial magnetization equal to one. In the M0 IC case the relaxation to equilibrium is almost exponential, while,for M1 IC, when correlations and aging are found, the decay is a power-law and the overall behavior can be very well reproduced by a Tsallis q-exponential function. These results contribute to clarify the overall scenario, which is more complex than previously expected and stress the importance of the dynamics in the relaxation process. The nonextensive statistical mechanics formalism proposed by Tsallis seems to be valid, in the out-of-equilibrium phase, when correlations and strong long-term memory effects emerge. This regime becomes stable if the $N\to \infty $ limit is performed before the $t\to \infty $ limit.

cond-mat.stat-mech↗