Related papers: Hopfield models as generalized random mean field m…

The low-temperature phase of discontinuous mean-field spin glasses is generally described by a one-step replica symmetry breaking (1RSB) Ansatz. The Gardner transition, i.e. a very-low-temperature phase transition to a full replica symmetry…

We study the structure of the ground states of local stoquastic Hamiltonians and show that under mild assumptions the following distributions can efficiently approximate one another: (a) distributions arising from ground states of…

We investigate families of generalized mean--field theories that can be formulated using the Peierls--Bogoliubov inequality. For test--Hamiltonians describing mutually non--interacting subsystems of increasing size, the thermodynamics of…

We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…

We derive the thermodynamic limit of the empirical correlation and response functions in the Langevin dynamics for spherical mixed $p$-spin disordered mean-field models, starting uniformly within one of the spherical bands on which the…

We study a paradigmatic system with long-range interactions: the Hamiltonian Mean-Field Model (HMF). It is shown that in the thermodynamic limit this model does not relax to the usual equilibrium Maxwell-Boltzmann distribution. Instead, the…

We investigate steady states of macroscopic quantum systems under dissipation not obeying the detailed balance condition. We argue that the Gibbs state at an effective temperature gives a good description of the steady state provided that…

We show that finite systems whose Hamiltonians obey a generalized homogeneity relation rigorously follow the nonextensive thermostatistics of Tsallis. In the thermodynamical limit, however, our results indicate that the Boltzmann-Gibbs…

We describe in detail two numerical simulation methods valid to study systems whose thermostatistics is described by generalized entropies, such as Tsallis. The methods are useful for applications to non-trivial interacting systems with a…

We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we…

A longstanding open question in the theory of disordered systems is whether short-range models, such as the random field Ising model or the Edwards-Anderson model, can indeed have the famous properties that characterize mean-field spin…

In this paper, we show that the empirical measure of mean-field model satisfies the large deviation principle with respect to the weak convergence topology or the stronger Wasserstein metric, under the strong exponential integrability…

Analysis of extremal behavior of stochastic processes is a key ingredient in a wide variety of applications, including probability, statistical physics, theoretical computer science, and learning theory. In this paper, we consider centered…

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…

In this work we discuss a short range version of the $p$-spin model. The model is provided with a parameter that allows to control the crossover with the mean field behaviour. We detect a discrepancy between the perturbative approach and…

We investigate thermodynamic phase transitions of the joint presence of spin glass (SG) and random field (RF) using a random graph model that allows us to deal with the quenched disorder. Therefore, the connectivity becomes a controllable…

We study a one-dimensional version of the Hopfield model with long, but finite range interactions below the critical temperature. In the thermodynamic limit we obtain large deviation estimates for the distribution of the ``local'' overlaps,…

Gibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many…

The processes of interplant competition within a field are still poorly understood. However, they explain a large part of the heterogeneity in a field and may have longer-term consequences, especially in mixed stands. Modeling can help to…

We study a ``two-pattern'' Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and we find that the metastate is supported on an infinity of symmetric pairs of pure…