Related papers: Near optimal configurations in mean field disorder…
Counting the number of ground states for a spin-glass or NP-complete combinatorial optimization problem is even more difficult than the already hard task of finding a single ground state. In this paper the entropy of minimum vertex-covers…
In a spin glass system on a random graph, some vertices have their spins changing among different configurations of a ground--state domain. Long range frustrations may exist among these unfrozen vertices in the sense that certain…
We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from -1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed…
For the statistics of global observables in disordered systems, we discuss the matching between typical fluctuations and large deviations. We focus on the statistics of the ground state energy $E_0$ in two types of disordered models : (i)…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington-Kirkpatrick (SK) mean field spin glass. We measure the probability distribution of the overlap among quenched configurations and…
Mean-field models of glasses that present a random first order transition exhibit highly non-trivial fluctuations. Building on previous studies that focused on the critical scaling regime, we here obtain a fully quantitative framework for…
Many scientific problems seek to find the ground state in a rugged energy landscape, a task that becomes prohibitively difficult for large systems. Within a particular class of problems, however, the short-range correlations within energy…
Shortened abstract: A mean field theory of long range frustration is constructed for spin glass systems with quenched randomness of vertex--vertex connections and of spin--spin coupling strengths. This theory is applied to a spin glass…
We present a numerical study of ground states of the dilute versions of the Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called "sparse" mean-field spin glasses that have been studied widely on random networks of…
We use energy landscape methods to investigate the response of a supercooled liquid to random pinning. We classify the structural similarity of different energy minima using a measure of overlap. This analysis reveals a correspondence…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
A disordered system is denominated `annealed' when the interactions themselves may evolve and adjust their values to lower the free energy. The opposite (`quenched') situation when disorder is fixed, is the one relevant for physical…
This work explores the global optimization problem of finding lowest-energy configurations (ground states) in disordered continuous spins models from statistical physics, with a particular focus on the random field XY model. Due to an…
Using a stochastic algorithm introduced in a previous paper, we study the finite size volume corrections and the fluctuations of the ground state energy in the Sherrington-Kirkpatrick and the Edwards-Anderson models at zero temperature. The…
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…
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…
We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters.…
The free energy of the Random Energy Model at the transition point between ferromagnetic and spin glass phases is calculated. At this point, equivalent to the decoding error threshold in optimal codes, free energy has finite size…