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F. Ritort

Publications and source records attributed to F. Ritort.

At least 55 records · Page 3Linked to original sources
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

A two-state kinetic model for the unfolding of single molecules by mechanical force

We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate), and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results (Liphardt, J., et al. (2002) {\em Science}, {\bf 296} 1832-1835). We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within $k_BT$, from non-equilibrium experiments using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, $\bar{\Wdis}$, to $k_BT$.}

physics.bio-ph↗
arXiv2001

The disordered Backgammon model

In this paper we consider an exactly solvable model which displays glassy behavior at zero temperature due to entropic barriers. The new ingredient of the model is the existence of different energy scales or modes associated to different relaxational time-scales. Low-temperature relaxation takes place by partial equilibration of successive lower energy modes. An adiabatic scaling solution, defined in terms of a threshold energy scale $\eps^*$, is proposed. For such a solution, modes with energy $\eps\gg\eps^*$ are equilibrated at the bath temperature, modes with $\eps\ll\eps^*$ remain out of equilibrium and relaxation occurs in the neighborhood of the threshold $\eps\sim \eps^*$. The model is presented as a toy example to investigate conditions related to the existence of an effective temperature in glassy systems and its possible dependence on the energy sector probed by the corresponding observable.

cond-mat.stat-mech↗
arXiv2001

The Nearest and Next Nearest Neighbor Sherrington-Kirkpatrick Model

The mean field theory of a spin glass with a specific form of nearest and next nearest neighbor interactions is investigated. Depending on the sign of the interaction matrix chosen we either find the continuous replica symmetry breaking seen in the Sherrington-Kirkpartick model or a one step solution similar to that found in structural glasses. Our results are confirmed by numerical simulations and the link between the type of spin-glass behavior and the density of eigenvalues of the interaction matrix is discussed.

cond-mat.dis-nn↗
arXiv2001

Random energy levels and low-temperature expansions for spin glasses

In a previous paper (cond-mat/0106554) we showed the existence of two new zero-temperature exponents (λand θ') in two dimensional Gaussian spin glasses. Here we introduce a novel low-temperature expansion for spin glasses expressed in terms of the gap probability distributions for successive energy levels. After presenting the numerical evidence in favor of a random-energy levels scenario, we analyze the main consequences on the low-temperature equilibrium behavior. We find that the specific heat is anomalous at low-temperatures c ~ T**αwith α=-d/θ' which turns out to be linear for the case θ'=-d.

cond-mat.dis-nn↗
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.

cond-mat.dis-nn↗
arXiv2001

Statistics of lowest excitations in two dimensional Gaussian spin glasses

A detailed investigation of lowest excitations in two-dimensional Gaussian spin glasses is presented. We show the existence of a new zero-temperature exponent lambda describing the relative number of finite-volume excitations with respect to large-scale ones. This exponent yields the standard thermal exponent of droplet theory theta through the relation, theta=d(lambda-1). Our work provides a new way to measure the thermal exponent theta without any assumption about the procedure to generate typical low-lying excitations. We find clear evidence that theta < theta_{DW} where theta_{DW} is the thermal exponent obtained in domain-wall theory showing that MacMillan excitations are not typical.

cond-mat.dis-nn↗
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.

cond-mat.soft↗
arXiv2001

Chaotic, memory and cooling rate effects in spin glasses: Is the Edwards-Anderson model a good spin glass?

We investigate chaotic, memory and cooling rate effects in the three dimensional Edwards-Anderson model by doing thermoremanent (TRM) and AC susceptibility numerical experiments and making a detailed comparison with laboratory experiments on spin glasses. In contrast to the experiments, the Edwards-Anderson model does not show any trace of re-initialization processes in temperature change experiments (TRM or AC). A detailed comparison with AC relaxation experiments in the presence of DC magnetic field or coupling distribution perturbations reveals that the absence of chaotic effects in the Edwards-Anderson model is a consequence of the presence of strong cooling rate effects. We discuss possible solutions to this discrepancy, in particular the smallness of the time scales reached in numerical experiments, but we also question the validity of the Edwards-Anderson model to reproduce the experimental results.

cond-mat.dis-nn↗
arXiv2000

Inherent structures and non-equilibrium dynamics of 1D constrained kinetic models: a comparison study

e discuss the relevance of the Stillinger and Weber approach to the glass transition investigating the non-equilibrium behavior of models with non-trivial dynamics, but with simple equilibrium properties. We consider a family of 1D constrained kinetic models, which interpolates between the asymmetric chain introduced by Eisinger and Jäckle [Z. Phys. {\bf B84}, 115 (1991)] and the symmetric chain introduced by Fredrickson and Andersen [Phys. Rev. Lett {\bf 53}, 1244 (1984)], and the 1D version of the Backgammon model [Phys. Rev. Lett. {\bf 75}, 1190 (1995)]. We show that the configurational entropy obtained from the inherent structures is the same for all models irrespective of their different microscopic dynamics. We present a detailed study of the coarsening behavior of these models, including the relation between fluctuations and response. Our results suggest that any approach to the glass transition inspired by mean-field ideas and resting on the definition of a configurational entropy must rely on the absence of any growing characteristic coarsening pattern.

cond-mat.stat-mech↗
arXiv2000

Activated processes and Inherent Structure dynamics of finite-size mean-field models for glasses

We investigate the inherent structure (IS) dynamics of mean-field {\it finite-size} spin-glass models whose high-temperature dynamics is described in the thermodynamic limit by the schematic Mode Coupling Theory for super-cooled liquids. Near the threshold energy the dynamics is ruled by activated processes which induce a logarithmic slow relaxation. We show the presence of aging in both the IS correlation and integrated response functions and check the validity of the one-step replica symmetry breaking scenario in the presence of activated processes. Our work shows: 1) The violation of the fluctuation-dissipation theorem is given by the configurational entropy, 2) The intermediate time regime ($\log(t)\sim N$) in mean-field theory automatically includes activated processes opening the way to analytically investigate activated processes by computing corrections beyond mean-field.

cond-mat.dis-nn↗
arXiv2000

Potential energy landscape of finite-size mean-field models for glasses

connected spin-glass models with a discontinuous transition. In the thermodynamic limit the equilibrium properties in the high temperature phase are described by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it finite-size} fully connected spin-glass models do exhibit properties typical of Lennard-Jones systems when both are near the critical glass transition, where thermodynamics is ruled by energy minima distribution. Our study opens the way to consider activated processes in real glasses through finite-size corrections (i.e. calculations beyond the saddle point approximation) in mean-field spin-glass models.

cond-mat.dis-nn↗
arXiv2000

Exact solutions and dynamics of globally coupled phase oscillators

We analyze mean-field models of synchronization of phase oscillators with singular couplings and subject to external random forces. They are related to the Kuramoto-Sakaguchi model. Their probability densities satisfy local partial differential equations similar to the Porous Medium, Burgers and extended Burgers equations depending on the degree of singularity of the coupling. We show that Porous Medium oscillators (the most singularly coupled) do not synchronize and that (transient) synchronization is possible only at zero temperature for Burgers oscillators. The extended Burgers oscillators have a nonlocal coupling first introduced by Daido and they may synchronize at any temperature. Exact expressions for their synchronized phases and for Daido's order function are given in terms of elliptic functions.

nlin.AO↗
arXiv1999

Equilibrium and Aging Dynamics of Simple Models for Glasses

We analyze the properties of the energy landscape of {\it finite-size} fully connected $p$-spin-like models. In the thermodynamic limit the high temperature phase is described by the schematic Mode Coupling Theory of super-cooled liquids. In this limit the barriers between different basins are infinite below the critical dynamical temperature the ergodicity is broken on in infinite times. We show that {\it finite-size} fully connected $p$-spin-like models, where activated processes are possible, do exhibit properties typical of real super-cooled liquid when both are near the critical glass transition. Our results support the conclusion that fully-connected $p$-spin-like models are the natural statistical mechanical models for studying the glass transition in super-cooled liquids.

cond-mat.stat-mech↗
arXiv1999

Are Mean-Field Spin-Glass Models Relevant for the Structural Glass Transition?

We analyze the properties of the energy landscape of {\it finite-size} fully connected p-spin-like models whose high temperature phase is described, in the thermodynamic limit, by the schematic Mode Coupling Theory of super-cooled liquids. We show that {\it finite-size} fully connected p-spin-like models, where activated processes are possible, do exhibit properties typical of real super-cooled liquid when both are near the critical glass transition. Our results support the conclusion that fully-connected p-spin-like models are the natural statistical mechanical models for studying the glass transition in super-cooled liquids.

cond-mat.dis-nn↗
arXiv1999

Damage spreading transition in glasses: a probe for the ruggedness of the configurational landscape

We consider damage spreading transitions in the framework of mode-coupling theory. This theory describes relaxation processes in glasses in the mean-field approximation which are known to be characterized by the presence of an exponentially large number of meta-stable states. For systems evolving under identical but arbitrarily correlated noises we demonstrate that there exists a critical temperature $T_0$ which separates two different dynamical regimes depending on whether damage spreads or not in the asymptotic long-time limit. This transition exists for generic noise correlations such that the zero damage solution is stable at high-temperatures being minimal for maximal noise correlations. Although this dynamical transition depends on the type of noise correlations we show that the asymptotic damage has the good properties of an dynamical order parameter such as: 1) Independence on the initial damage; 2) Independence on the class of initial condition and 3) Stability of the transition in the presence of asymmetric interactions which violate detailed balance. For maximally correlated noises we suggest that damage spreading occurs due to the presence of a divergent number of saddle points (as well as meta-stable states) in the thermodynamic limit consequence of the ruggedness of the free energy landscape which characterizes the glassy state. These results are then compared to extensive numerical simulations of a mean-field glass model (the Bernasconi model) with Monte Carlo heat-bath dynamics. The freedom of choosing arbitrary noise correlations for Langevin dynamics makes damage spreading a interesting tool to probe the ruggedness of the configurational landscape.

cond-mat.dis-nn↗
arXiv1999

Absence of aging in the remanent magnetization in Migdal-Kadanoff spin glasses

We study the non-equilibrium behavior of three-dimensional spin glasses in the Migdal-Kadanoff approximation, that is on a hierarchical lattice. In this approximation the model has an unique ground state and equilibrium properties correctly described by the droplet model. Extensive numerical simulations show that this model lacks aging in the remanent magnetization as well as a maximum in the magnetic viscosity in disagreement with experiments as well as with numerical studies of the Edwards-Anderson model. This result strongly limits the validity of the droplet model (at least in its simplest form) as a good model for real spin glasses.

cond-mat.dis-nn↗