Related papers: Numerical study of ground state energy fluctuation…
Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of…
There are many ways of establishing upper bounds on fluctuations of random variables, but there is no systematic approach for lower bounds. As a result, lower bounds are unknown in many important problems. This paper introduces a general…
We propose a self-consistent Ornstein-Zernike approximation for studying the Edwards-Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations…
We introduce "AnnealSGD", a regularized stochastic gradient descent algorithm motivated by an analysis of the energy landscape of a particular class of deep networks with sparse random weights. The loss function of such networks can be…
We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the…
It is generally believed (but not yet proved) that Ising spin glasses with nearest-neighbor interactions have a phase transition in three and higher dimensions to a low-temperature spin glass phase, but the nature of this phase remains…
As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and…
In this paper we look at a class of random optimization problems that arise in the forms typically known in statistical physics as Little models. In \cite{BruParRit92} the Little models were studied by means of the well known tool from the…
We consider the dynamics of spin facilitated models of glasses in the non-equilibrium aging regime following a sudden quench from high to low temperatures. We briefly review known results obtained for the broad class of kinetically…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
We present a thorough numerical analysis of the relaxational dynamics of the Sherrington-Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes $N$. In the thermodynamic limit and at low…
We analyze the Blume-Emery-Griffiths model with disordered magnetic interaction displaying the inverse freezing phenomenon. The behaviour of this spin-1 model in crystal field is studied throughout the phase diagram and the transition and…
Using an efficient polynomial-time ground state algorithm we investigate the Ising spin glass state at zero temperature in two dimensions. For large sizes, we show that the spin state in a central region is independent of the interactions…
We numerically study finite-dimensional spin glasses at low and zero temperature, finding evidences for (i) strong time/space heterogeneities, (ii) spontaneous time scale separation and (iii) power law distributions of flipping times. Using…
The free energy landscape of the Sherrington-Kirkpatrik (SK) Ising spin glass is simple in the framework of the Thouless-Anderson-Palmer (TAP) equations as each solution (which are minima of the free energy) has associated with it a nearby…
We examined energy spectrums of some particular systems of binary spins. It is shown that the configuration space can be divided into classes, and in the limit the energy distributions in these classes can be approximated by the normal…
We investigate the performance of the recently proposed stationary Fokker-Planck sampling method considering a combinatorial optimization problem from statistical physics. The algorithmic procedure relies upon the numerical solution of a…
We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma\sigma'}(r)$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational…
We study numerically various properties of the free energy barriers in the Edwards-Anderson model of spin glasses in the low-temperature region both in three and four spatial dimensions. In particular, we investigated the dependence of…
Based on the modified Thouless-Anderson-Palmer equations a detailed numerical investigation for the complexity of the Sherrington-Kirkpatrick spin glass is worked out. The data suggest a scaling law which leads to a vanishing of the…