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Giorgio Parisi

Publications and source records attributed to Giorgio Parisi.

At least 217 records · Page 12Linked to original sources
arXiv2002

Spin glasses on Bethe Lattices for large coordination number

We study spin glasses on random lattices with finite connectivity. In the infinite connectivity limit they reduce to the Sherrington Kirkpatrick model. In this paper we investigate the expansion around the high connectivity limit. Within the replica symmetry breaking scheme at two steps, we compute the free energy at the first order in the expansion in inverse powers of the average connectivity (z), both for the fixed connectivity and for the fluctuating connectivity random lattices. It is well known that the coefficient of the 1/z correction for the free energy is divergent at low temperatures if computed in the one step approximation. We find that this annoying divergence becomes much smaller if computed in the framework of the more accurate two steps breaking. Comparing the temperature dependance of the coefficients of this divergence in the replica symmetric, one step and two steps replica symmetry breaking, we conclude that this divergence is an artefact due to the use of a finite number of steps of replica symmetry breaking. The 1/z expansion is well defined also in the zero temperature limit.

cond-mat.dis-nn↗
arXiv2002

The physical Meaning of Replica Symmetry Breaking

In this talk I will presente the physical meaning of replica symmetry breaking stressing the physical concepts. After introducing the theoretical framework and the experimental evidence for replica symmetry breaking, I will describe some of the basic ideas using a probabilistic language. The predictions for off-equilibrium dynamics will be shortly outlined.

cond-mat.stat-mech↗
arXiv2002

Geometric approach to the dynamic glass transition

We numerically study the potential energy landscape of a fragile glassy system and find that the dynamic crossover corresponding to the glass transition is actually the effect of an underlying geometric transition caused by a qualitative change in the topological properties of the landscape. Furthermore, we show that the potential energy barriers connecting local glassy minima increase with decreasing energy of the minima, and we relate this behaviour to the fragility of the system. Finally, we analyze the real space structure of activated processes by studying the distribution of particle displacements for local minima connected by simple saddles.

cond-mat.dis-nn↗
arXiv2001

Role of saddles in mean-field dynamics above the glass transition

Recent numerical developments in the study of glassy systems have shown that it is possible to give a purely geometric interpretation of the dynamic glass transition by considering the properties of unstable saddle points of the energy. Here we further develop this program in the context of a mean-field model, by analytically studying the properties of the closest saddle point to an equilibrium configuration of the system. We prove that when the glass transition is approached the energy of the closest saddle goes to the threshold energy, defined as the energy level below which the degree of instability of the typical stationary points vanishes. Moreover, we show that the distance between a typical equilibrium configuration and the closest saddle is always very small and that, surprisingly, it is almost independent of the temperature.

cond-mat.stat-mech↗
arXiv2001

Growing length scales in a supercooled liquid close to an interface

We present the results of molecular dynamics computer simulations of a simple glass former close to an interface between the liquid and the frozen amorphous phase of the same material. By investigating F_s(q,z,t), the incoherent intermediate scattering function for particles that have a distance z from the wall, we show that the relaxation dynamics of the particles close to the wall is much slower than the one for particles far away from the wall. For small z the typical relaxation time for F_s(q,z,t) increases like exp(Delta/(z-z_p)), where Delta and z_p are constants. We use the location of the crossover from this law to the bulk behavior to define a first length scale tilde{z}. A different length scale is defined by considering the Ansatz F_s(q,z,t) = F_s^{bulk}(q,t) +a(t) exp[-(z/xi(t))^{beta(t)}], where a(t), xi(t), and beta(t) are fit parameters. We show that this Ansatz gives a very good description of the data for all times and all values of z. The length xi(t) increases for short and intermediate times and decreases again on the time scale of the alpha-relaxation of the system. The maximum value of xi(t) can thus be defined as a new length scale xi_max. We find that tilde{z} as well as xi_max increase with decreasing temperature. The temperature dependence of this increase is compatible with a divergence of the length scale at the Kauzmann temperature of the bulk system.

cond-mat.stat-mech↗
arXiv2001

Fast Monte Carlo algorithm for supercooled soft spheres

We present a nonlocal Monte Carlo algorithm with particle swaps that greatly accelerates thermalization of soft sphere binary mixtures in the glassy region. Our first results show that thermalization of systems of hundreds of particles is achievable, and find behavior compatible with a thermodynamic glass transition.

cond-mat.dis-nn↗
arXiv2001

Planck's Legacy to Statistical Mechanics

In this talk I will describe the deep influence Planck had on the development of statistical mechanics. At this end I will first outline the theoretical situation of statistical mechanics before Planck. I will then describe his main contributions to this field and the progresses obtained as an immediate consequence of his work. I will also outline the later evolution of statistical mechanics in relation with Planck's work. I will finally report on a still unsolved problem in statistical mechanics, historically related to the properties of black-body radiation.

cond-mat.stat-mech↗
arXiv2000

The Bethe lattice spin glass revisited

So far the problem of a spin glass on a Bethe lattice has been solved only at the replica symmetric level, which is wrong in the spin glass phase. Because of some technical difficulties, attempts at deriving a replica symmetry breaking solution have been confined to some perturbative regimes, high connectivity lattices or temperature close to the critical temperature. Using the cavity method, we propose a general non perturbative solution of the Bethe lattice spin glass problem at a level of approximation which is equivalent to a one step replica symmetry breaking solution. The results compare well with numerical simulations. The method can be used for many finite connectivity problems appearing in combinatorial optimization.

cond-mat.dis-nn↗
arXiv2000

Stochastic Stability

In this talk I will introduce the principle of stochastic stability and discussing its consequences both at equilibrium and off-equilibrium.

cond-mat.stat-mech↗
arXiv2000

Comment on "Liquid Limits: The Glass Transition and Liquid-Gas Spinodal Boundaries of Metastable Liquids"

In ref. cond-mat/0005372, Sastry studies by numerical simulations the phase diagram of a simple fragile glass-forming liquid, presenting very interesting and clear results. We apply to this system, at various density values, the analytic approach to structural glass thermodynamics recently introduced and we compare our theoretical predictions on the liquid-glass transition temperature with Sastry's data.

cond-mat.dis-nn↗
arXiv2000

Non trivial overlap distributions at zero temperature

We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non trivial overlap probability distribution among the unperturbed ground state and the one in presence of the coupling. We find a closed formula for this probability for arbitrary ultrametric trees, in terms of the parameters defining the tree. The same probability is computed in numerical simulations of a simple model with many ground states, but no ultrametricity: polymers in random media in 1+1 dimension. This gives us an idea of what violation of our formula can be expected in cases when ultrametricity does not hold.

cond-mat.dis-nn↗
arXiv2000

On nonlinear susceptibility in supercooled liquids

In this paper, we discuss theoretically the behavior of the four point nonlinear susceptibility and its associated correlation length for supercooled liquids close to the Mode Coupling instability temperature $T_c$. We work in the theoretical framework of the glass transition as described by mean field theory of disordered systems, and the hypernetted chain approximation. Our results give an interpretation framework for recent numerical findings on heterogeneities in supercooled liquid dynamics.

cond-mat.dis-nn↗
arXiv2000

On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.

cond-mat.dis-nn↗
arXiv2000

On the Energy Minima of the SK Model

We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and the quenched energy, looking at the dependence on the starting equilibrium temperature, and performing a systematic analysis of finite size effects.

cond-mat.dis-nn↗
arXiv2000

Toy model for the mean-field theory of hard-sphere liquids

We investigate a toy model of liquid, based on simplified HNC equations in very large spatial dimension D. The model does not exhibit a phase transition, but several regimes of the behavior when D\to\infty can be observed in different intervals of the density.

cond-mat.stat-mech↗
arXiv2000

Statistical Physics of Structural Glasses

This paper gives an introduction and brief overview of some of our recent work on the equilibrium thermodynamics of glasses. We have focused onto first principle computations in simple fragile glasses, starting from the two body interatomic potential. A replica formulation translates this problem into that of a gas of interacting molecules, each molecule being built of $m$ atoms, and having a gyration radius (related to the cage size) which vanishes at zero temperature. We use a small cage expansion, valid at low temperatures, which allows to compute the cage size, the specific heat (which follows the Dulong and Petit law), and the configurational entropy. The no-replica interpretation of the computations is also briefly described. The results, particularly those concerning the Kauzmann tempaerature and the configurational entropy, are compared to recent numerical simulations.

cond-mat.dis-nn↗