arXiv subjects

A. Crisanti

Publications and source records attributed to A. Crisanti.

At least 37 records · Page 2Linked to original sources

arXiv2007

Reply to Comment on ``Spherical 2+p spin-glass model: an analytically solvable model with a glass-to-glass transition''

In his Comment, Krakoviack [Phys. Rev. B (2007)] finds that the phase behavior of the s+p spin-glass model is different from what proposed by Crisanti and Leuzzi [Phys. Rev. B 73, 014412 (2006)] if s and p are larger than two and are separated well enough. He proposes a trial picture, based on a one step replica symmetry breaking solution, displaying a mode-coupling-like glass-to-glass transition line ending in a A3 singularity. However, actually, the physics of these systems changes when p-s is large, the instability of which the one step replica symmetry breaking glassy phase suffers turns out to be so wide ranging that the whole scenario proposed by Krakoviack must be seriously reconsidered.

cond-mat.dis-nn↗

arXiv2006

On Equilibrium Dynamics of Spin-Glass Systems

We present a critical analysis of the Sompolinsky theory of equilibrium dynamics. By using the spherical $2+p$ spin glass model we test the asymptotic static limit of the Sompolinsky solution showing that it fails to yield a thermodynamically stable solution. We then present an alternative formulation, based on the Crisanti, Hörner and Sommers [Z. für Physik {\bf 92}, 257 (1993)] dynamical solution of the spherical $p$-spin spin glass model, reproducing a stable static limit that coincides, in the case of a one step Replica Symmetry Breaking Ansatz, with the solution at the dynamic free energy threshold at which the relaxing system gets stuck off-equilibrium. We formally extend our analysis to any number of Replica Symmetry Breakings $R$. In the limit $R\to\infty$ both formulations lead to the Parisi anti-parabolic differential equation. This is the special case, though, where no dynamic blocking threshold occurs. The new formulation does not contain the additional order parameter $Δ$ of the Sompolinsky theory.

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arXiv2004

The spherical $2+p$ spin glass model: an exactly solvable model for glass to spin-glass transition

We present the full phase diagram of the spherical $2+p$ spin glass model with $p\geq 4$. The main outcome is the presence of a new phase with both properties of Full Replica Symmetry Breaking (FRSB) phases of discrete models, e.g, the Sherrington-Kirkpatrick model, and those of One Replica Symmetry Breaking (1RSB). The phase, which separates a 1RSB phase from FRSB phase, is described by an order parameter function $q(x)$ with a continuous part (FRSB) for $x<m$ and a discontinuous jump (1RSB) at $x=m$. This phase has a finite complexity which leads to different dynamic and static properties.

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arXiv2004

Complexity in Mean-Field Spin-Glass Models: Ising $p$-spin

The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one step Replica Symmetry Breaking. Two solutions of the resulting saddle point equations are found. One is supersymmetric (SUSY) and includes the equilibrium value of the free energy while the other is non-SUSY. The two solutions cross exactly at a value of the free energy where the replicon eigenvalue is zero; at low free energy the complexity is described by the SUSY solution while at high free energy it is described by the non-SUSY solution. In particular the non-SUSY solution describes the total number of solutions, like in the Sherrington-Kirkpatrick (SK) model. The relevant TAP solutions corresponding to the non-SUSY solution share the same feature of the corresponding solutions in the SK model, in particular their Hessian has a vanishing isolated eigenvalue. The TAP solutions corresponding to the SUSY solution, instead, are well separated minima.

cond-mat.stat-mech↗

arXiv2004

Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model

The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz corresponds to require Becchi-Rouet-Stora-Tyutin supersymmetry. The complexity computed this way is the Legendre transform of the free energy averaged over the quenched disorder. The stability analysis shows that this complexity is inconsistent at any free energy level but the equilibirum one. The further problem of building a physically well defined solution not invariant under supersymmetry and predicting an extensive number of metastable states is also discussed.

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arXiv2003

On Spin-Glass Complexity

We study the quenched complexity in spin-glass mean-field models satisfying the Becchi-Rouet-Stora-Tyutin supersymmetry. The outcome of such study, consistent with recent numerical results, allows, in principle, to conjecture the absence of any supersymmetric contribution to the complexity in the Sherrington-Kirkpatrick model. The same analysis can be applied to any model with a Full Replica Symmetry Breaking phase, e.g. the Ising $p$-spin model below the Gardner temperature. The existence of different solutions, breaking the supersymmetry, is also discussed.

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arXiv2003

The Complexity of the Spherical $p$-spin spin glass model, revisited

Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general calculation procedure which is discussed step-by-step.

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arXiv2003

Intermittency of glassy relaxation and the emergence of a non-equilibrium spontaneous measure in the aging regime

We consider heat exchange processes between non-equilibrium aging systems (in their activated regime) and the thermal bath in contact. We discuss a scenario where two different heat exchange processes concur in the overall heat dissipation: a stimulated fast process determined by the temperature of the bath and a spontaneous intermittent process determined by the fact that the system has been prepared in a non-equilibrium state. The latter is described by a probability distribution function (PDF) that has an exponential tail of width given by a parameter $λ$, and satisfies a fluctuation theorem (FT) governed by that parameter. The value of $λ$ is proportional to the so-called effective temperature, thereby providing a practical way to experimentally measure it by analyzing the PDF of intermittent events.

cond-mat.soft↗

arXiv2003

Complexity of the Sherrington-Kirkpatrick Model in the Annealed Approximation

A careful critical analysis of the complexity, at the annealed level, of the Sherrington-Kirkpatrick model has been performed. The complexity functional is proved to be always invariant under the Becchi-Rouet-Stora-Tyutin supersymmetry, disregarding the formulation used to define it. We consider two different saddle points of such functional, one satisfying the supersymmetry [A. Cavagna {\it et al.}, J. Phys. A {\bf 36} (2003) 1175] and the other one breaking it [A.J. Bray and M.A. Moore, J. Phys. C {\bf 13} (1980) L469]. We review the previews studies on the subject, linking different perspectives and pointing out some inadequacies and even inconsistencies in both solutions.

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arXiv2003

Frequency-domain study of relaxation in a spin glass model for the structural glass transition

We have computed the time-dependent susceptibility for the finite-size mean-field Random Orthogonal model (ROM). We find that for temperatures above the mode-coupling temperature the imaginary part of the susceptibility $χ''(ν)$ obeys the scaling forms proposed for glass-forming liquids. Furthermore, as the temperature is lowered the peak frequency of $χ''$ decreases following a Vogel-Fulcher law with a critical temperature remarkably close to the known critical temperature $T_c$ where the configurational entropy vanishes.

cond-mat.stat-mech↗

arXiv2003

On the Parisi-Toulouse hypothesis for the spin glass phase in mean-field theory

We consider the spin-glass phase of the Sherrington-Kirkpatrick model in the presence of a magnetic field. The series expansion of the Parisi function $q(x)$ is computed at high orders in powers of $τ=T_c-T$ and $H$. We find that none of the Parisi-Toulouse scaling hypotheses on the $q(x)$ behavior strictly holds, although some of them are violated only at high orders. The series is resummed yielding results in the whole spin-glass phase which are compared with those from a numerical evaluation of the $q(x)$. At the high order considered, the transition turns out to be third order on the Almeida-Thouless line, a result which is confirmed rigorously computing the expansion of the solution near the line at finite $τ$. The transition becomes smoother for infinitesimally small field while it is third order at strictly zero field.

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arXiv2003

Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence

This review reports on the research done during the past years on violations of the fluctuation-dissipation theorem (FDT) in glassy systems. It is focused on the existence of a quasi-fluctuation-dissipation theorem (QFDT) in glassy systems and the currently supporting knowledge gained from numerical simulation studies. It covers a broad range of non-stationary aging and stationary driven systems such as structural-glasses, spin-glasses, coarsening systems, ferromagnetic models at criticality, trap models, models with entropy barriers, kinetically constrained models, sheared systems and granular media. The review is divided into four main parts: 1) An introductory section explaining basic notions related to the existence of the FDT in equilibrium and its possible extension to the glassy regime (QFDT), 2) A description of the basic analytical tools and results derived in the framework of some exactly solvable models, 3) A detailed report of the current evidence in favour of the QFDT and 4) A brief digression on the experimental evidence in its favour. This review is intended for inexpert readers who want to learn about the basic notions and concepts related to the existence of the QFDT as well as for the more expert readers who may be interested in more specific results.

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arXiv2003

A New Method to Compute the Configurational Entropy in Spin Glasses

We propose a new method to compute the configurational entropy of glassy systems as a function of the free energy of valleys at a given temperature, in the framework of the Stillinger and Weber approach. In this method, which we call free-energy inherent structures (FEIS) approach, valleys are represented by inherent structures that are statistically grouped according to their free-energy rather than the energy as is commonly done in the standard procedure. The FEIS method provides a further step toward a description of the relaxational behavior of glassy systems in terms of a free energy measure. It can be used to determine the character of the glass transition as well as the mode coupling and the Kauzmann temperatures. We illustrate the usefulness of the method by applying it to simple models of glasses and spin glasses.

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arXiv2002

Is the Stillinger and Weber decomposition relevant for coarsening models?

We study three kinetic models with constraint, namely the Symmetrically Constrained Ising Chain, the Asymmetrically Constrained Ising Chain, and the Backgammon Model. All these models show glassy behavior and coarsening. We apply to them the Stillinger and Weber decomposition, and find that they share the same configurational entropy, despite of their different nonequilibrium dynamics. We conclude therefore that the Stillinger and Weber decomposition is not relevant for this type of models.

cond-mat.stat-mech↗

arXiv2002

Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model

In this work we analyse the Parisi's infinity-replica symmetry breaking solution of the Sherrington - Kirkpatrick model without external field using high order perturbative expansions. The predictions are compared with those obtained from the numerical solution of the infinity-replica symmetry breaking equations which are solved using a new pseudo-spectral code which allows for very accurate results. With this methods we are able to get more insight into the analytical properties of the solutions. We are also able to determine numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T --> 0} x_{max}(T) > 0.5.

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arXiv2001

Inherent Structures, Configurational Entropy and Slow Glassy Dynamics

We give a short introduction to the inherent structure approach, with particular emphasis on the Stillinger and Weber decomposition, of glassy systems. We present some of the results obtained in the framework of spin-glass models and Lennard-Jones glasses. We discuss how to generalize the standard Stillinger and Weber approach by including the entropy of inherent structures. Finally we discuss why this approach is probably insufficient to describe the behavior of some kinetically constrained models.

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arXiv2001

The 3-SAT problem with large number of clauses in $\infty$-replica symmetry breaking scheme

In this paper we analyze the structure of the UNSAT-phase of the overconstrained 3-SAT model by studying the low temperature phase of the associated disordered spin model. We derive the $\infty$ Replica Symmetry Broken equations for a general class of disordered spin models which includes the Sherrington - Kirkpatrick model, the Ising $p$-spin model as well as the overconstrained 3-SAT model as particular cases. We have numerically solved the $\infty$ Replica Symmetry Broken equations using a pseudo-spectral code down to and including zero temperature. We find that the UNSAT-phase of the overconstrained 3-SAT model is of the $\infty$-RSB kind: in order to get a stable solution the replica symmetry has to be broken in a continuous way, similarly to the SK model in external magnetic field.

cond-mat.stat-mech↗

arXiv2001

A glass transition scenario based on heterogeneities and entropy barriers

We propose a scenario for the glass transition based on the cooperative nature of nucleation processes and entropic effects. The main point is the relation between the off-equilibrium energy dissipation and nucleation processes in off-equilibrium supercooled liquids which leads to a natural definition of the complexity. From the absence of coarsening growth we can derive an entropy based fluctuation formula which relates the free energy dissipation rate in the glass with the nucleation rate of the largest cooperative regions. As by-product we obtain a new phenomenological relation between the largest relaxation time in the supercooled liquid phase and an effective temperature. This differs from the Adam-Gibbs relation in that predicts no divergence of the primary relaxation time at the Kauzmann temperature and the existence of a crossover from fragile to strong behavior.

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