Related papers: Finite-size relaxational dynamics of a spike rando…
Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick…
These notes give an introduction to the physics of the infinite range version of the Edwards--Anderson model, the so-called Sherrington--Kirkpatrick model. In a first part, I motivate and introduce the Edwards--Anderson and…
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron and structural glasses. A…
In this note we study the zero temperature dynamics of the Sherrington Kirkppatric model and we investigate the statistical properties of the configurations that are obtained in the large time limit. We find that the replica symmetry is…
For the statistics of global observables in disordered systems, we discuss the matching between typical fluctuations and large deviations. We focus on the statistics of the ground state energy $E_0$ in two types of disordered models : (i)…
In a recent work (Eissfeller and Opper, 1992) a numerical method has been proposed to simulate off-equilibrium zero-temperature parallel dynamics for the SK model without finite size effects. We study the extension of the method to non-zero…
Fine resolution of the discrete eigenvalues at the spectral edge of an $N\times N$ random matrix is required in many applications. Starting from a finite-size scaling ansatz for the Stieltjes transform of the maximum likelihood spectrum, we…
We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad…
We study how the finite-sized n-component model A with periodic boundary conditions relaxes near its bulk critical point from an initial nonequilibrium state with short-range correlations. Particular attention is paid to the universal…
The ground-state energy E_0 of a spin glass is an example of an extreme statistic. We consider the large deviations of this energy for a variety of models when the number of spins N goes to infinity. In most cases, the behavior can be…
We consider a simple, purely stochastic model characterized by two conserved quantities (mass density $a$ and energy density $h$) which is known to display a condensation transition when $h > 2a^2$: in the localized phase a single site…
The Sherrington-Kirkpatrick (SK) is a foundational model for understanding spin glass systems. It is based on the pairwise interaction between each two spins in a fully connected lattice with quenched disordered interactions. The nature of…
We discuss a general formalism that allows study of transitions over barriers in spin glasses with long-range interactions that contain large but finite number, $N$, of spins. We apply this formalism to the Sherrington-Kirkpatrick model…
We argue that when the number of spins $N$ in the SK model is finite, the Parisi scheme can be terminated after $K$ replica-symmetry breaking steps, where $K(N) \propto N^{1/6}$. We have checked this idea by Monte Carlo simulations: we…
We consider the spherical Sherrington-Kirkpatrick model of spin glass with sparse interaction, where the interactions between most of the pairs of the spin variables are possibly zero. With suitable normalization, we prove that the limiting…
The spherical Sherrington-Kirkpatrick model is a spherical mean field model for spin glass. We consider the fluctuations of the free energy at arbitrary non-critical temperature for the 2-spin model with no magnetic field. We show that in…
We present the results of a molecular dynamics computer simulation in which we investigate the dynamics of silica. By considering different system sizes, we show that in simulations of the dynamics of this strong glass former surprisingly…
We consider the probability distribution of large deviations in the spin-glass free energy for the Sherrington-Kirkpatrick mean field model, i.e. the exponentially small probability of finding a system with intensive free energy smaller…
Facilitated spin models on random graphs provide an ideal microscopic realization of the mode-coupling theory of supercooled liquids: they undergo a purely dynamic glass transition with no thermodynamic singularity. In this paper we study…
We perform a systematic analytical study of finite size effects in separable recurrent neural network models with sequential dynamics, away from saturation. We find two types of finite size effects: thermal fluctuations, and…