Calculation of ground states of four-dimensional +or- J Ising spin glasses

Abstract

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 as e_0=-2.095(1). The ground-state stiffness (or domain wall) energy D is calculated. A D~L^Θ behavior with Θ=0.65(4) is found which confirms that the d=4 model has an equilibrium spin-glass-paramagnet transition for non-zero T_c.

5 pages, 3 figures, 31 references, revtex; update of references

References in corpus (1)

• Comment on "Evidence for nontrivial ground-state structure of 3d +/- J spin glasses"

Cited by in corpus (40)

• Optimization with Extremal Dynamics
• Geometrical Aspects of Aging and Rejuvenation in the Ising Spin Glass: A Numerical Study
• Nature of the Spin Glass State
• Monte Carlo Simulations of Spin Glasses at Low Temperatures
• Extremal Optimization for Graph Partitioning
• Lower Critical Dimension of Ising Spin Glasses
• Energy exponents and corrections to scaling in Ising spin glasses
• Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses
• Finding Low-Temperature States with Parallel Tempering, Simulated Annealing and Simple Monte Carlo
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
• Interface energies in Ising spin glasses
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• Temperature Chaos and Bond Chaos in the Edwards-Anderson Ising Spin Glass : Domain-Wall Free-Energy Measurements
• Improved extremal optimization for the Ising spin glass
• Stiffness Exponents for Lattice Spin Glasses in Dimensions d=3,...,6
• Low-Temperature Excitations of Dilute Lattice Spin Glasses
• Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses
• Extended droplet theory for aging in short-ranged spin glasses and a numerical examination
• Ground states of two-dimensional $\pm$J Edwards-Anderson spin glasses
• Jamming Model for the Extremal Optimization Heuristic
• Correlation Length of the Two-Dimensional Ising Spin Glass with Gaussian Interactions
• Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field
• The influence of critical behavior on the spin glass phase
• Monte Carlo simulations of spin glasses at low temperatures: Effects of free boundary conditions
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Optimizing at the Ergodic Edge
• Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions
• The nature of ergodicity breaking in Ising spin glasses as revealed by correlation function spectral properties
• Extensive eigenvalues in spin-spin correlations: a tool for counting pure states in Ising spin glasses
• Ordered phase in the two-dimensional randomly coupled ferromagnet
• Direct sampling of complex landscapes at low temperatures: the three-dimensional +/-J Ising spin glass
• Order-parameter fluctuations in Ising spin glasses at low temperatures
• Reduction of Two-Dimensional Dilute Ising Spin Glasses
• No spin-glass transition in the "mobile-bond" model
• Excitations in high-dimensional random-field Ising magnets
• The Eigenvalue Analysis of the Density Matrix of 4D Spin Glasses Supports Replica Symmetry Breaking
• Ferromagnetic-spin glass transition in four-dimensional random-bond Ising model
• Exact Ground States of the Kaya-Berker Model
• Global Minimum Depth In Edwards-Anderson Model