相关论文: About the de Almeida-Thouless line in neural netwo…
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…
We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines and we solve for its quenched free energy, in the thermodynamic limit and allowing for a first step of replica symmetry breaking.…
We use the generic replica symmetric cubic field-theory to study the transition of short range Ising spin glasses in a magnetic field around the upper critical dimension, d=6. A novel fixed-point is found, in addition to the well-known zero…
We investigate an XY spin-glass model in which both spins and couplings evolve in time: the spins change rapidly according to Glauber-type rules, whereas the couplings evolve slowly with a dynamics involving spin correlations and Gaussian…
The similarities between Hartree-Fock (HF) theory and the density-matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function ansatz. Linearization of the…
We investigate an XY spin-glass model in which both spins and interactions (or couplings) evolve in time, but with widely separated time-scales. For large times this model can be solved using replica theory, requiring two levels of…
We present a Physics-Informed Neural Network (PINN) framework for reconstructing the redshift-dependent Hubble parameter \(H(z)\) within the Tsallis Holographic Dark Energy (THDE) model extended by massive neutrinos. In this approach, the…
Spin glass systems as lattices of disordered magnets with random interactions have important implications within the theory of magnetization and applications to a wide-range of hard combinatorial optimization problems. Nevertheless, despite…
We test four fast mean field type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low temperature regime, the simulated annealing…
We discuss a phase transition in spin glass models which have been rarely considered in the past, namely the phase transition that may take place when two real replicas are forced to be at a larger distance (i.e. at a smaller overlap) than…
We apply the renormalized perturbation theory (RPT) to the symmetric Anderson impurity model. Within the RPT framework exact results for physical observables such as the spin and charge susceptibility can be obtained in terms of the…
We generalize the de Almeida-Thouless line for the many-body Ising spin glass to the microcanonical ensemble and show that it coincides with the canonical one. This enables us to draw a complete microcanonical phase diagram of this model.
We study the Hopfield model with pure $p$-spin interactions with even $p\geq 4$, and a number of patterns, M(N) growing with the system size, $N$, as $M(N) = \a N^{p-1}$. We prove the existence of a critical temperature $\b_p$ characterized…
We show that the only solutions of the TAP equations for the Sherrington-Kirkpatrick model of Ising spin glasses which can be found by iteration are those whose free energy lies on the border between replica symmetric and broken replica…
The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the…
This work finds its place in the statistical mechanical approach to light amplification in disordered media, namely Random Lasers (RLs). The problem of going beyond the standard mean-field Replica Symmetry Breaking (RSB) theory employed to…
In this paper we study, via equilibrium statistical mechanics, the properties of the internal energy of an Hopfield neural network whose patterns are stored continuously (Gaussian distributed). The model is shown to be equivalent to a…
We report on the ensemble inequivalence in a many-body spin-glass model with integer spin. The spin-glass phase transition is of first order for certain values of the crystal field strength and is dependent whether it was derived in the…
Recently a daily routine for associative neural networks has been proposed: the network Hebbian-learns during the awake state (thus behaving as a standard Hopfield model), then, during its sleep state, optimizing information storage, it…
We introduce a spin-1 version of the random energy model with crystal field. Crystal field controls the density of 0 spins in the system. We solve the model in the micro-canonincal ensemble. The model has a spin-glass transition at a finite…