相关论文: Random-cluster correlation inequalities for Gibbs …

We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures $\beta=1/T=50$. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping…

We present a detailed proof of a previously announced result (C.M. Newman and D.L. Stein, Phys. Rev. Lett. v. 84, pp. 3966--3969 (2000)) supporting the absence of multiple (incongruent) ground state pairs for 2D Edwards-Anderson spin…

The growing correlation length observed in supercooled liquids as their temperature is lowered has been studied with the aid of a single occupancy cell model. This model becomes more accurate as the density of the system is increased. One…

In this paper, we show that the replica symmetry of the Gibbs measure of spherical spin systems is a property of the eigenvalue spacing at the edge of the interaction matrix. In particular, our interaction matrix has \textbf{two} large…

The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between…

Spin-glasses are natural Gibbs distributions that have been studied in Theoretical CS for many decades. Recently, they have been gaining attention from the community as they emerge naturally in neural computation and learning, network…

We study the Gibbs measure of mixed spherical $p$-spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on…

In this paper we prove the weak convergence, in a high-temperature phase, of the finite marginals of the Gibbs measure associated to a symmetric spherical spin glass model with correlated couplings towards an explicit asymptotic decoupled…

We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show…

Mean field spin glass models have undergone substantial mathematical development, but finite dimensional short range spin glasses remain much less understood. This paper proves several rigorous zero temperature signatures of glassy behavior…

We consider percolation properties of the Boolean model generated by a Gibbs point process and balls with deterministic radius. We show that for a large class of Gibbs point processes there exists a critical activity, such that percolation…

Spin-glasses are Gibbs distributions that have been studied in CS for many decades. Recently, they have gained renewed attention as they emerge naturally in learning, inference, optimisation etc. We consider the Edwards-Anderson (EA)…

Infinite-range spin-glass models with Levy-distributed interactions show a spin-glass transition with similarities to both the Sherrington-Kirkpatrick model and to disordered spin systems on finite connectivity random graphs. Despite the…

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…

We present the results of Monte Carlo simulations of two different Potts glass models with short range random interactions. In the first model a \pm J-distribution of the bonds is chosen, in the second model a Gaussian distribution. In both…

We present a new and simple approach to concentration inequalities for functions around their expectation with respect to non-product measures, i.e., for dependent random variables. Our method is based on coupling ideas and does not use…

We consider the free energy difference restricted to a finite volume for certain pairs of incongruent thermodynamic states (if they exist) in the Edwards-Anderson Ising spin glass at nonzero temperature. We prove that the variance of this…

We investigate scenarios in which the low-temperature phase of short-range spin glasses comprises thermodynamic states which are nontrivial mixtures of multiple incongruent pure state pairs. We construct a new kind of metastate supported on…

We show that under a low complexity condition on the gradient of a Hamiltonian, Gibbs distributions on the Boolean hypercube are approximate mixtures of product measures whose probability vectors are critical points of an associated…

We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range…