arXiv subjects

Andrea Crisanti

Publications and source records attributed to Andrea Crisanti.

30 records · Page 2Linked to original sources

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

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↗

arXiv2003

Frequency-domain study of $α$-relaxation in the Random Orthogonal Model

The time-dependent susceptibility for the finite-size mean-field Random Orthogonal model (ROM) is studied numerically for temperatures above the mode-coupling temperature. The results show that the imaginary part of the susceptibility $χ''(ν)$ obeys the scaling form proposed for glass-forming liquids with the peak frequency decreasesing as the temperature is lowered consistently with the Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature $T_c$ of the model where the configurational entropy vanishes.

cond-mat.dis-nn↗

arXiv2002

Chaos in temperature in the Sherrington-Kirkpatrick model

We prove the existence of chaos in temperature in the Sherringhton-Kirkpatrick model. The effect is exceedingly small, namely of the ninth order in perturbation theory. The equations describing two systems at different temperatures constrained to have a fixed overlap are studied analytically and numerically, yielding information about the behaviour of the overlap distribution function $P_{T_1,T_2}(q)$ in finite-size systems.

cond-mat.dis-nn↗

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

A real-space description of the glass transition based on heterogeneities and entropy barriers

An alternative scenario for the glass transition based on the cooperative nature of nucleation processes and the role of entropic effects is presented. The new ingredient is to relate the dissipation during the relaxation process to the release of strain energy driven by the nucleation of progressively larger cooperative spatial regions. Using an equiprobability hypothesis for the transition between different metastable configurations, we obtain a relation between the free energy dissipation rate and the size of the largest cooperative regions. Th is leads to a new phenomenological relation between the largest relaxation time in the supercooled liquid phase and the effective temperature. This differs from the classical Adam-Gibbs relation in that predicts no divergence of the primary relaxation time at the Kauzmann temperature but a crossover from fragile to strong behavior.

cond-mat.stat-mech↗

arXiv2000

Configurational entropy and the one-step RSB scenario in glasses

In this talk we discuss the possibility of constructing a fluctuation theory for structural glasses in the non-equilibrium aging state. After reviewing well known results in a toy model we discuss some of the key assumptions which support the validity of this theory, in particular the role of the configurational entropy and its relation to the effective temperature. Recent numerical results for mean-field finite-size glasses agree with this scenario.

cond-mat.dis-nn↗

arXiv1997

A Soluble Phase Field Model

The kinetics of an initially undercooled solid-liquid melt is studied by means of a generalized Phase Field model, which describes the dynamics of an ordering non-conserved field phi (e.g. solid-liquid order parameter) coupled to a conserved field (e.g. thermal field). After obtaining the rules governing the evolution process, by means of analytical arguments, we present a discussion of the asymptotic time-dependent solutions. The full solutions of the exact self-consistent equations for the model are also obtained and compared with computer simulation results. In addition, in order to check the validity of the present model we confronted its predictions against those of the standard Phase field model and found reasonable agreement. Interestingly, we find that the system relaxes towards a mixed phase, depending on the average value of the conserved field, i.e. on the initial condition. Such a phase is characterized by large fluctuations of the phi field.

cond-mat↗

arXiv1994

Critical behavior of nonequilibrium q-state systems

We present two classes of nonequilibrium models with critical behavior. Each model is characterized by an integer $q>1$, and is defined on configurations of $q$-valued spins on regular lattices. The definitions of the models are very similar to the updating rules in Wolff's algorithm for the Potts model, but both classes break detailed balance, except for $q=2$ and $q=\infty$. In the first case both models reduce to the Ising model, while one of them reduces to percolation (more precisely, to the general epidemic process) for $q=\infty$. Locations of the critical point and critical exponents are estimated in 2 dimensions.

cond-mat↗