arXiv subjects

Luca Leuzzi

Publications and source records attributed to Luca Leuzzi.

At least 55 records · Page 3Linked to original sources

arXiv2013

Critical behavior of the XY model in complex topologies

The critical behavior of the O(2) model on dilute Levy graphs built on a 2D square lattice is analyzed. Different qualitative cases are probed, varying the exponent rho governing the dependence on the distance of the connectivity probability distribution. The mean-field regime, as well as the long-range and short-range non-mean-field regimes are investigated by means of high-performance parallel Monte-Carlo numerical simulations running on GPUs. The relationship between the long-range rho exponent and the effective dimension of an equivalent short-range system with the same critical behavior is investigated. Evidence is provided for the effective short-range dimension to coincide with the spectral dimension of the Levy graph for the XY model in the mean-field regime.

cond-mat.stat-mech↗

arXiv2013

Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field

The Ising model in a random field and with power-law decaying ferromagnetic bonds is studied at zero temperature. Comparing the scaling of the energy contributions of the ferromagnetic domain wall flip and of the random field a la Imry-Ma we obtain a threshold value for the power $ρ$ of the long-range interaction, beyond which no critical behavior occurs. The critical threshold value is $ρ_c=3/2$, at a difference with the zero field model in which $ρ_c=2$. This prediction is confirmed by numerical computation of the ground states below, at, and above this threshold value. Some possible implications for the critical behavior of spin-glasses in a field are conjectured.

cond-mat.dis-nn↗

arXiv2013

Exactly solvable spin-glass models with ferromagnetic couplings: the spherical multi-$p$-spin model in a self-induced field

We report some results on the quenched disordered Spherical multi-$p$-Spin Model in presence of ferromagnetic couplings. In particular, we present the phase diagrams of some representative cases that schematically describe, in the mean-field approximation, the behavior of most known transitions in glassy materials, including dynamic arrest in super-cooled liquids, amorphous-amorphous transitions and spin-glass transitions. A simplified notation is introduced in order to compute systems properties in terms of an effective, self-induced, field encoding the whole ferromagnetic information.

cond-mat.dis-nn↗

arXiv2012

Shaken Granular Lasers

Granular materials have been studied for decades, also driven by industrial and technological applications. These very simple systems, composed by agglomerations of mesoscopic particles, are characterized, in specific regimes, by a large number of metastable states and an extreme sensitivity (e.g., in sound transmission) on the arrangement of grains; they are not substantially affected by thermal phenomena, but can be controlled by mechanical solicitations. Laser emission from shaken granular matter is so far unexplored; here we provide experimental evidence that it can be affected and controlled by the status of motion of the granular, we also find that competitive random lasers can be observed. We hence demonstrate the potentialities of gravity affected moving disordered materials for optical applications, and open the road to a variety of novel interdisciplinary investigations, involving modern statistical mechanics and disordered photonics.

physics.optics↗

arXiv2012

Following states in temperature in the spherical s+p-spin glass model

In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the spherical $s+p$-spin glass model, extending the work of Barrat, Franz and Parisi J. Phys. A 30, 5593 (1997). We confirm the presence of level crossings, bifurcations, and temperature chaos. For the states that are at equilibrium close to the so-called dynamical temperature $T_d$, we find, however, that the following state method (and the dynamical solution of the model as well) is intrinsically limited by the vanishing of solutions with non-zero overlap at low temperature.

cond-mat.dis-nn↗

arXiv2012

Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models

An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the power- law decay exponents in the β regime. In the original structural glass context this relationship follows from the MCT equations that are obtained making rather uncontrolled approximations and λ has to be treated like a tunable parameter. It is known that a certain class of mean-field spin-glass models is exactly described by MCT equations. In this context, the physical meaning of the so called parameter exponent λ has recently been unveiled, giving a method to compute it exactly in a static framework. In this paper we exploit this new technique to compute the critical slowing down exponents in a class of mean-field Ising spin-glass models including, as special cases, the Sherrington-Kirkpatrick model, the p-spin model and the Random Orthogonal model.

cond-mat.dis-nn↗

arXiv2012

On the two-steps relaxation of mean-field glasses: p-spin model

Critical slowing down dynamics of supercooled glass-forming liquids is usually understood at the mean-field level in the framework of Mode Coupling Theory, providing a two-time relaxation scenario and power-law behaviors of the time correlation function at dynamic criticality. In this work we derive critical slowing down exponents of spin-glass models undergoing discontinuous transitions by computing their Gibbs free energy and connecting the dynamic behavior to static "in-state" properties. Both the spherical and Ising versions are considered and, in the simpler spherical case, a generalization to arbitrary schematic Mode Coupling kernels is presented. Comparison with dynamic results available in literature is performed. Analytical predictions for the Ising case are provided for any $p$.

cond-mat.dis-nn↗

arXiv2011

Statistical mechanical approach to secondary processes and structural relaxation in glasses and glass formers

The interrelation of dynamic processes active on separated time-scales in glasses and viscous liquids is investigated using a model displaying two time-scale bifurcations both between fast and secondary relaxation and between secondary and structural relaxation. The study of the dynamics allows for predictions on the system relaxation above the temperature of dynamic arrest in the mean-field approximation, that are compared with the outcomes of the equations of motion directly derived within the Mode Coupling Theory (MCT) for under-cooled viscous liquids. Varying the external thermodynamic parameters a wide range of phenomenology can be represented, from a very clear separation of structural and secondary peak in the susceptibility loss to excess wing structures.

cond-mat.dis-nn↗

arXiv2011

Random, thermodynamic and inverse first order transitions in the Blume-Capel spin-glass

The spherical mean field approximation of a spin-1 model with p-body quenched disordered interaction is investigated. Depending on temperature and chemical potential the system is found in a paramagnetic or in a glassy phase and the transition between these phases can be of different nature. In given conditions inverse freezing occurs. As $p=2$ the glassy phase is replica symmetric and the transition is always continuous in the phase diagram. For $p>2$ the exact solution for the glassy phase is obtained by the one step replica symmetry breaking Ansatz. Different scenarios arise for both the dynamic and the thermodynamic transitions. These include (i) the usual random first order transition (Kauzmann-like) preceded by a dynamic transition, typical of mean-field glasses, (ii) a thermodynamic first order transition with phase coexistence and latent heat and (iii) a regime of inversion of static and dynamic transition lines. In the latter case a thermodynamic stable glassy phase, with zero configurational entropy, is dynamically accessible from the paramagnetic phase. Crossover between different transition regimes are analyzed by means of Replica Symmetry Breaking theory and a detailed study of the complexity and of the stability of the static solution is performed throughout the space of external thermodynamic parameters.

cond-mat.dis-nn↗

arXiv2010

The overlap parameter across an inverse first order phase transition in a 3D spin-glass

We investigate the thermodynamic phase transition taking place in the Blume-Capel model in presence of quenched disorder in three dimensions (3D). In particular, performing Exchange Montecarlo simulations, we study the behavior of the order parameters accross the first order phase transition and its related coexistence region. This transition is an Inverse Freezing.

cond-mat.dis-nn↗

arXiv2010

Complexity of waves in nonlinear disordered media

The statistical properties of the phases of several modes nonlinearly coupled in a random system are investigated by means of a Hamiltonian model with disordered couplings. The regime in which the modes have a stationary distribution of their energies and the phases are coupled is studied for arbitrary degrees of randomness and energy. The complexity versus temperature and strength of nonlinearity is calculated. A phase diagram is derived in terms of the stored energy and amount of disorder. Implications in random lasing, nonlinear wave propagation and finite temperature Bose-Einstein condensation are discussed.

cond-mat.stat-mech↗

arXiv2010

Thermodynamic first order transition and inverse freezing in a 3D spin-glass

We present a numerical study of the random Blume-Capel model in three dimension. The phase diagram is characterized by spin-glass/paramagnet phase transitions both of first and second order in the thermodynamic sense. Numerical simulations are performed using the Exchange-Monte Carlo algorithm, providing clear evidence for inverse freezing. The main features at criticality and in the phase coexistence region are investigated. We are not privy to other 3D short-range systems with quenched disorder undergoing inverse freezing.

cond-mat.dis-nn↗

arXiv2008

A stroll among effective temperatures in aging systems: limits and perspectives

In this paper we present a short survey on the concept of effective temperature, on its onset as a glass former vitrifies, on the various definitions in literature and their limits of applicability. An exactly solvable model glass is employed to compare effective temperatures among them and to set a criterion for the occurrence of a universal extra temperature in the framework of a "two temperature thermodynamics" for off-equilibrium aging systems. It will be shown that aging in glass formers is not a sufficient requirement. As an instance, memory effects typical of glasses are not compatible with a unique effective temperature. Yet, a reduced range of applicability can still be established and investigated.

cond-mat.dis-nn↗

arXiv2008

Static and dynamic glass-glass transitions: a mean-field study

The behavior of a family of mean-field glass models is reviewed. The models are analyzed by means of a Langevin-based approach to the dynamics and a Replica theory computation of the thermodynamics. We focus on the phase diagram of a particular model case, where glass-to-glass transitions occur between phases with a different number of characteristic time-scales for the relaxation processes. The appearence of Johari-Goldstein processes as collective reorganizations of sets of fast processes is discussed.

cond-mat.dis-nn↗

arXiv2007

Amorphous-amorphous transition and the two-step replica symmetry breaking phase

The nature of polyamorphism and amorphous-to-amorphous transition is investigated by means of an exactly solvable model with quenched disorder, the spherical s+p multi-spin interaction model. The analysis is carried out in the framework of Replica Symmetry Breaking theory and leads to the identification of low temperature glass phases of different kinds. Besides the usual `one-step' solution, known to reproduce all basic properties of structural glasses, also a physically consistent `two-step' solution arises. More complicated phases are found as well, as temperature is further decreased, expressing a complex variety of metastable states structures for amorphous systems.

cond-mat.dis-nn↗

arXiv2006

Marginal States in Mean Field Glasses

We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In particular, we give a physical interpretation of the two-group replica symmetry breaking scheme and confirm it by establishing the relation to the cavity method and to the counting of solutions of the Thouless-Anderson-Palmer equations. We show how these methods all incorporate the presence of a soft mode in the free energy landscape and interpret the occurring order parameter functions in terms of correlations between the soft mode and the local magnetizations. The general formalism is applied to the prototypical case of the Sherrington-Kirkpatrick-model where we re-examine the physical properties of marginal states under a new perspective.

cond-mat.dis-nn↗

arXiv2005

Kovacs effect in solvable model glasses

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs and applied on glassy polymers, is implemented in an exactly solvable model with facilitated dynamics. This model is based on interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property and to slow dynamics, the model reproduces the characteristic non-monotonic evolution known as the ``Kovacs effect'', observed in polymers, spin glasses, in granular materials and models of molecular liquids, when similar experimental protocols are implemented.

cond-mat.dis-nn↗

arXiv2005

Kovacs Effect in a Fragile Glass Model

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs for glassy polymers, is implemented in an exactly solvable dynamical model. This model is characterized by interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property, the model reproduces the characteristic non-monotonic evolution known as the ``Kovacs effect'', observed in polymers, in granular materials and models of molecular liquids, when similar experimental protocols are implemented.

cond-mat.dis-nn↗