arXiv subjects

Luca Leuzzi

Publications and source records attributed to Luca Leuzzi.

61 records · Page 4Linked to original sources

arXiv2005

Stable Solution of the Simplest Spin Model for Inverse Freezing

We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction that displays the inverse freezing phenomenon. The behavior of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and spinodal lines for the model are computed using the Full Replica Symmetry Breaking Ansatz that always yields a thermodynamically stable phase. We compare the results both with the formulation of the same model in terms of Ising spins on lattice gas, where no reentrance takes place, and with the model with generalized spin variables recently introduced by Schupper and Shnerb [Phys. Rev. Lett. {\bf 93} 037202 (2004)], for which the reentrance is enhanced as the ratio between the degeneracy of full to empty sites increases. The simplest version of all these models, known as the Ghatak-Sherrington model, turns out to hold all the general features characterizing an inverse transition to an amorphous phase, including the right thermodynamic behavior.

cond-mat.dis-nn↗

arXiv2005

The spherical 2+p spin glass model: an analytically solvable model with a glass-to-glass transition

We present the detailed analysis of the spherical s+p spin glass model with two competing interactions: among p spins and among s spins. The most interesting case is the 2+p model with p > 3 for which a very rich phase diagram occurs, including, next to the paramagnetic and the glassy phase represented by the one step replica symmetry breaking ansatz typical of the spherical p-spin model, other two amorphous phases. Transitions between two contiguous phases can also be of different kind. The model can thus serve as mean-field representation of amorphous-amorphous transitions (or transitions between undercooled liquids of different structure). The model is analytically solvable everywhere in the phase space, even in the limit where the infinite replica symmetry breaking ansatz is required to yield a thermodynamically stable phase.

cond-mat.stat-mech↗

arXiv2004

Thermodynamic Properties and Phase Transitions in a Mean-Field Ising Spin Glass on Lattice Gas: the Random Blume-Emery-Griffiths-Capel Model

The study of the mean-field static solution of the Random Blume-Emery-Griffiths-Capel model, an Ising-spin lattice gas with quenched random magnetic interaction, is performed. The model exhibits a paramagnetic phase, described by a stable Replica Symmetric solution. When the temperature is decreased or the density increases, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value, of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and accompanied by a latent heat. In this last case coexistence of phases takes place. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme, and the relative Parisi equations are solved using a pseudo-spectral method down to zero temperature.

cond-mat.stat-mech↗

arXiv2002

First Order Phase Transition and Phase Coexistence in a Spin-Glass Model

We study the mean-field static solution of the Blume-Emery-Griffiths-Capel model with quenched disorder, an Ising-spin lattice gas with quenched random magnetic interaction. The thermodynamics is worked out in the Full Replica Symmetry Breaking scheme. The model exhibits a high temperature/low density paramagnetic phase. When the temperature is decreased or the density increased, the system undergoes a phase transition to a Full Replica Symmetry Breaking spin-glass phase. The nature of the transition can be either of the second order (like in the Sherrington-Kirkpatrick model) or, at temperature below a given critical value (tricritical point), of the first order in the Ehrenfest sense, with a discontinuous jump of the order parameter and a latent heat. In this last case coexistence of phases occurs.

cond-mat.stat-mech↗

arXiv2001

Inherent Structures in models for fragile and strong glass

An analysis of the dynamics is performed, of exactly solvable models for fragile and strong glasses, exploiting the partitioning of the free energy landscape in inherent structures. The results are compared with the exact solution of the dynamics, by employing the formulation of an effective temperature used in literature. Also a new formulation is introduced, based upon general statistical considerations, that performs better. Though the considered models are conceptually simple there is no limit in which the inherent structure approach is exact.

cond-mat.stat-mech↗

arXiv2001

Effective temperatures in an exactly solvable model for a fragile glass

A model glass is considered with one type of fast ($β$-type) of processes, and one type of slow processes ($α$-type). On time-scales where the fast ones are in equilibrium, the slow ones have a dynamics that resembles the one of facilitated spin models. The main features are the occurrence of a Kauzmann transition, a Vogel-Fulcher-Tammann-Hesse behaviour for the relaxation time, an Adam-Gibbs relation between relaxation time and configurational entropy, and an aging regime. The model is such that its statics is simple and its (Monte-Carlo-type) dynamics is exactly solvable. The dynamics has been studied both on the approach to the Kauzmann transition and below it. In certain parameter regimes it is so slow that it sets out a quasi-equilibrium at a time dependent effective temperature. Correlation and Response functions are also computed, as well as the out of equilibrium Fluctuation-Dissipation Relation, showing the uniqueness of the effective temperature, thus giving support to the rephrasing of the problem within the framework of out of equilibrium thermodynamics.

cond-mat.stat-mech↗

arXiv1999

Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions

Ising spin-glass systems with long-range interactions ($J(r)\sim r^{-σ}$) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution of the overlaps and of the ultrametric structure of the space of the equilibrium configurations in the frozen phase. Also in presence of diverging thermodynamical fluctuations at the critical point the behaviour of the model is shown to be of the Replica Simmetry Breaking type and there are hints of a non-trivial ultrametric structure. The parallel tempering algorithm has been used to simulate the dynamical approach to equilibrium of such systems.

cond-mat.dis-nn↗