Related papers: Ground State Structure in a Highly Disordered Spin…
Ground states of the Edwards-Anderson (EA) spin glass model are studied on infinite graphs with finite degree. Ground states are spin configurations that locally minimize the EA Hamiltonian on each finite set of vertices. A problem with…
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…
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…
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.…
We study the stability of ground states in the Edwards-Anderson Ising spin glass in dimensions two and higher against perturbations of a single coupling. After reviewing the concepts of critical droplets, flexibilities and metastates, we…
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…
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…
Ground states of four-dimensional (d=4) EA Ising spin glasses are calculated for sizes up to 7x7x7x7 using a combination of a genetic algorithm and cluster-exact approximation. The ground-state energy of the infinite system is extrapolated…
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…
We investigate numerically disorder chaos in spin glasses, i.e. the sensitivity of the ground state to small changes of the random couplings. Our study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We find that in all…
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 study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from…
We rigorously rule out the appearance of multiple domain walls between ground states in 2D Edwards-Anderson Ising spin glasses (with periodic boundary conditions and, e.g., Gaussian couplings). This supports the conjecture that there is…
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…
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…
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…
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…
Positioned between crystalline solids and liquids, disordered many-particle systems which are stealthy and hyperuniform represent new states of matter that are endowed with novel physical and thermodynamic properties. Such stealthy and…
We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards-Anderson Ising model of a spin glass in arbitrary dimension. Given a specific ground state, suppose the coupling value…
We derive lower bounds for the variance of the difference of energies between incongruent ground states, i.e., states with edge overlaps strictly less than one, of the Edwards-Anderson model on ${\mathbb Z}^d$. The bounds highlight a…