Related papers: Optimizing glassy p-spin models
Finding an exact ground state of a three-dimensional (3D) Ising spin glass is proven to be an NP-hard problem (i.e., at least as hard as any problem in the nondeterministic polynomial-time (NP) class). Given validity of the exponential time…
We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins…
Due to an extremely rugged structure of the free energy landscape, the determination of spin-glass ground states is among the hardest known optimization problems, found to be NP-hard in the most general case. Owing to the specific structure…
Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed…
Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40^2. A combination of a genetic algorithm and Cluster-Exact Approximation is used. For…
Ground states of 3d EA Ising spin glasses are calculated for sizes up to $14^3$ using a combination of genetic algorithms and cluster-exact approximation . The distribution $P(|q|)$ of overlaps is calculated. For increasing size the width…
We consider whether it is possible to find ground states of frustrated spin systems by solving them locally. Using spin glass physics and Imry-Ma arguments in addition to numerical benchmarks we quantify the power of such local solution…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
The race to heuristically solve non-deterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which…
Ground states of three-dimensional EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained.…
The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly…
We present an algorithm which calculates groundstates of Ising spin glasses approximately. It works by randomly selecting clusters of spins which exhibit no frustrations. The spins which were not selected, contribute to the local fields of…
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…
Some questions concerning the calculation of the number of ``physical'' (metastable) states or complexity of the spherical $p$-spin spin glass model are reviewed and examined further. Particular attention is focused on the general…
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…
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 describe a numerical algorithm for computing spin glass ground states with a high level of reliability. The method uses a population based search and applies optimization on multiple scales. Benchmarks are given leading to estimates of…
A huge number of independent true ground-state configurations is calculated for two-, three- and four-dimensional +- J spin-glass models. Using the genetic cluster-exact approximation method, system sizes up to N=20^2,8^3,6^4 spins are…
We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining…
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…