Related papers: Ground State Structure in a Highly Disordered Spin…
The two-dimensional $S=1/2$ asymmetric Heisenberg Mattis model is investigated with the exact diagonalization of finite clusters. The N\'eel order parameter and the spin glass order parameter can be smoothly extrapolated to the…
We present an exact algorithm for finding all the ground states of the two-dimensional Edwards-Anderson $\pm J$ spin glass and characterize its performance. We investigate how the ground states change with increasing system size and and…
We investigate the conditions required for general spin systems with frustration and disorder to display self-organized criticality, a property which so far has been established only for the fully-connected infinite-range…
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…
Ground states of 3d EA Ising spin glasses are calculated for sizes up to 14^3 using a combination of a genetic algorithm and Cluster-Exact Approximation. Evidence for an ultrametric structure is found by studying triplets of independent…
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility,…
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…
For $L \times L$ square lattices with $L \le 20$ the 2D Ising spin glass with +1 and -1 bonds is found to have a strong correlation between the energy and the entropy of its ground states. A fit to the data gives the result that each…
We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that…
We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width…
We analyze the zero-temperature behavior of the XY Edwards-Anderson spin glass model on a square lattice. A newly developed algorithm combining exact ground-state computations for Ising variables embedded into the planar spins with a…
Recently extended precise numerical methods and droplet scaling arguments allow for a coherent picture of the glassy states of two-dimensional Ising spin glasses to be assembled. The length scale at which entropy becomes important and…
We consider the ferromagnetic Ising model on the Cayley tree and we investigate the decomposition of the free state into extremal states below the spin glass temperature. We show that this decomposition has uncountably many components. The…
We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow…
Ground-state properties of the two-dimensional $S=1/2$ random Heisenberg models are investigated by the exact-diagonalization method. The phase diagram of the bond-random model (the $\pm J$ model) is the same as that of the corresponding…
We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a…
We employ a novel algorithm using a quasi-exact embedded-cluster matching technique as minimization method within a genetic algorithm to reliably obtain numerically exact ground states of the Edwards-Anderson XY spin glass model with…
We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the…
We investigate the two-dimensional frustrated quantum Heisenberg model with bond disorder on nearest-neighbor couplings using the recently introduced Foundation Neural-Network Quantum States framework, which enables accurate and efficient…