Related papers: From local to global ground states in Ising spin g…
The chapter starts with a historical summary of first attempts to optimize the spin glass Hamiltonian, comparing it to recent results on searching largest cliques in random graphs. Exact algorithms to find ground states in generic spin…
Computing the ground state of Ising spin-glass models with p-spin interactions is, in general, an NP-hard problem. In this work we show that unlike in the case of the standard Ising spin glass with two-spin interactions, computing ground…
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…
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…
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…
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…
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…
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…
Spin glasses are disordered magnets with random interactions that are, generally, in conflict with each other. Finding the ground states of spin glasses is not only essential for the understanding of the nature of disordered magnetic and…
We derive exact analytical expressions for the ground-state energy and entropy of the two-dimensional $\pm J$ Ising spin glass, uncovering a nested hierarchy of frustrations. Each level in this hierarchy contributes through the kernel and…
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…
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 ``ballistic-search'' algorithm is presented which allows the identification of clusters (or funnels) of ground states in Ising spin glasses even for moderate system sizes. The clusters are defined to be sets of states, which are connected…
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…
Here we first discuss briefly the quantum annealing technique. We then study the quantum annealing of Sherrington-Kirkpatrick spin glass model with the tuning of both transverse and longitudinal fields. Both the fields are time-dependent…
Limited resources motivate decomposing large-scale problems into smaller,``local" subsystems and stitching together the so-found solutions. We explore the physics underlying this approach and discuss the concept of ``local hardness", i.e.,…
We show several calculations to identify the critical point in the ground state in random spin systems including spin glasses on the basis of the duality analysis. The duality analysis is a profound method to obtain the precise location of…
The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a…
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…
Although quantum annealing is usually considered as a method for locating the ground states of difficult spin-glass and optimization problems, its use in approximate optimization -- finding low- but not zero-energy states in a reasonably…