相关论文: Bounds for diluted mean-fields spin glass models
We study the Langevin dynamics for spherical $p$-spin models, focusing on the short time regime described by the Cugliandolo-Kurchan equations. Confirming a prediction of [Cugliandolo-Kurchan, Phys. Rev. Lett. 1993], we show the asymptotic…
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 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…
We study a multi-species spin glass system where the density of each species is kept fixed at increasing volumes. The model reduces to the Sherrington-Kirkpatrick one for the single species case. The existence of the thermodynamic limit is…
In this paper, we present a short proof of the limit of free energy of spherical 2 spin Sherrington-Kirkpatrick (SSK) model without external field. This proof works for all temperatures and is based on the Laplace method of integration and…
We consider the Sherrington-Kirkpatrick model and we prove that the thermodynamic limit of the quenched free energy per site is strictly greater than the corresponding replica symmetric approximation, for all values of the temperature and…
This review presents various aspects of a mean-field spin glass model known as the p-spin spherical spin glass model, which has raised a lot of interest in the study of spin glasses, and also for its possible links with a mean-field theory…
We analyze the coupled non-linear integro-differential equations whose solutions is the thermodynamical limit of the empirical correlation and response functions in the Langevin dynamics for spherical p-spin disordered mean-field models. 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…
We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models.…
We obtain bounds to show that the pressure of a two-body, mean-field spin glass is a Lipschitz function of the underlying distribution of the random coupling constants, with respect to a particular semi-norm. This allows us to re-derive a…
We consider the free energy of a mean-field quantum spin glass described by a $ p $-spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \infty $, i.e. the quantum random energy model (QREM), are…
We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(\sigma) = \sigma^T J \sigma$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles.…
We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \to \infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy…
In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific of this case are overcome introducing an…
Francesco Guerra and Fabio Toninelli have developped a very powerful technique to study the high temperature behaviour of the Sherrington-Kirkpatrick mean field spin glass model. They show that this model is asymptoticaly comparable to a…
We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called "sparse" mean-field spin glasses that have been studied widely on random networks of…
In two papers Franz, Leone and Toninelli proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution [5] and a general distribution [6]. Panchenko and Talagrand [16] simplified…
The low temperature phase of discontinuous mean-field spin glasses is characterized by the appearance of an exponential number of metastable states. Which ones among these states dominate the out-of-equilibrium dynamics of these systems? In…
We consider the quantum Sherrington-Kirkpatrick (SK) spin-glass model with transverse field and provide a formula for its free energy in the thermodynamic limit, valid for all inverse temperatures $\beta>0$. To characterize the free energy,…