Related papers: Exact Ground States of Large Two-Dimensional Plana…
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…
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…
Here we study the two-dimensional Kaya-Berker model, with a site occupancy p of one sub lattice, by using a polynomial-time exact ground-state algorithm. Thus, we were able to obtain T=0 results in exact equilibrium for rather large system…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large…
We propose a new method for exact analytical calculation of the ground-state energy of the Ising spin glass on strips. An outstanding advantage of this method over the numerical transfer matrix technique is that the energy is obtained for…
We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses. Our method is based on the computation of quenched free energies with periodic and twisted periodic boundary conditions on a finite basis.…
We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system,…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated…
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…
Spin glasses featured by frustrated interactions and metastable states have important applications in chemistry, material sciences and artificial neural networks. However, the solution of the spin glass models is hindered by the…
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 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 ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find…
We present exact ground states in spin models with orbital generacy in one and higher dimensions. A method to obtain the exact ground states of the models when the Hamiltonians are composed of the products of two commutable operators is…
Extensive computations of ground state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3,..,7. Results are presented for bond-densities exactly at the percolation threshold,…
We study the efficiency of parallel tempering Monte Carlo technique for calculating true ground states of the Edwards-Anderson spin glass model. Bimodal and Gaussian bond distributions were considered in two and three-dimensional lattices.…
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…
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…