相关论文: Beyond the Sherrington-Kirkpatrick Model

In this paper we study the phase diagram of a Sherrington-Kirkpatrick (SK) model where the couplings are forced to thermalize at different time scales. Besides being a challenging generalization of the SK model, such settings may arise…

We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a…

A growing body of evidence indicates that the sluggish low-temperature dynamics of glass formers (e.g. supercooled liquids, colloids or spin glasses) is due to a growing correlation length. Which is the effective field theory that describes…

We investigate the L\'evy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small couplings with a spare random backbone of strong bonds the…

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 survey the recent mathematical results about aging in certain simple disordered models. We start by the Bouchaud trap model. We then survey the results obtained for simple models of spin-glass dynamics, like the REM (the Random Energy…

The Parisi solution of the mean-field spin glass has been widely accepted and celebrated. Its marginal stability in 3d and its complexity however raised the question of its relevance to real spin glasses. This paper gives a short overview…

Some interesting recent advances in the theoretical understanding of neural networks have been informed by results from the physics of disordered many-body systems. Motivated by these findings, this work uses the replica technique to study…

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent…

Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and…

We review recent theoretical progress on glassy dynamics, with special emphasis on the importance and universality of the ``aging regime'', which is relevant to many experimental situations. The three main subjects which we address are: (i)…

We examine the phase diagram of the $p$-spin mean field glass model in the spin one case, that is when $S=0,+1,-1$. For large $p$ the model is solved exactly. The analysis reveals that the phase diagram is in some way similar to that of…

As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the…

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This…

We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order $m$. We compute the average or macroscopic spectral density in the limit of large matrix size, solving the…

We review recent progress in the mathematical theory of quantum disordered systems: the Anderson transition (joint work with Domingos Marchetti), the (quantum and classical) Edwards-Anderson (EA) spin glass model and return to equilibrium…

We present a new field theoretic approach for finite dimensional site disordered spin systems by introducing the notion of grand canonical disorder, where the number of spins in the system is random but quenched. We analyze this field…

We investigate generalized Sherrington--Kirkpatrick glassy systems without reflection symmetry. In the neighbourhood of the transition temperature we in general uncover the structure of the glass state building the full-replica-symmetry…

A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~…

We analyze operational risk in terms of a spin glass model. Several regimes are investigated, as a functions of the parameters that characterize the dynamics. The system is found to be robust against variations of these parameters. We…