相关论文: Spin-Glass Stochastic Stability: a Rigorous Proof

We present a detailed analysis for the Langevin dynamics of a spherical spin-glass model (the spherical Sherrington-Kirkpatrick model). All the spins in the system are coupled by pairs via a random interaction matrix taken from the Gaussian…

In previous work, we have developed a simple method to study the behavior of the Sherrington-Kirkpatrick mean field spin glass model for high temperatures, or equivalently for high external fields. The basic idea was to couple two different…

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with highly diversified collections of competing low energy states. The goal of this summary is to present some…

Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…

We describe our perspective on the Structural Glass Transition (SGT) problem built on the premise that a viable theory must provide a consistent picture of the dynamics and statics, which are manifested by large increase in shear viscosity…

The Potts spin glass is a generalization of the Sherrington--Kirkpatrick (SK) model that allows for spins to take more than two values. Based on a novel synchronization mechanism, Panchenko (2018) showed that the limiting free energy is…

The average ground state energies for spin glasses on Bethe lattices of connectivities r=3,...,15 are studied numerically for a Gaussian bond distribution. The Extremal Optimization heuristic is employed which provides high-quality…

We carry out an analysis of the effect of a quenched magnetic field on the dynamics of the spherical Sherrington-Kirkpatrick spin-glass model. We show that there is a characteristic time introduced by the presence of the field. Firstly, for…

A review of the stochastic stability property for the Gaussian spin glass models is presented and some perspectives discussed.

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…

Random Overlap Structures (ROSt's) are random elements on the space of probability measures on the unit ball of a Hilbert space, where two measures are identified if they differ by an isometry. In spin glasses, they arise as natural limits…

We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.

We derive analytical results for the large-time relaxation of the Sherrington - Kirkpatrick model in the thermodynamic limit, starting from a random configuration. The system never achieves local equilibrium in any fixed sector of…

Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the thermodynamics of mean-field models…

We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A…

In a $p$-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change in the course of time. The spins are coupled to a heat bath with temperature $T$, while the coupling constants are coupled to a bath…

Thermoremanent magnetization data for the 3D Edwards-Anderson spin glass are generated using the Waiting Time Method as simulational tool and interpreted using Record Dynamics. We verify that clusters of contiguous spins are overturned by…

The magnetic systems with disorder form an important class of systems, which are under intensive studies, since they reflect real systems. Such a class of systems is the spin glass one, which combines randomness and frustration. The…

We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach…