Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\dots ,8$ from Heuristic Ground State Optimization

Abstract

We present a collection of simulations of the Edwards-Anderson lattice spin glass at $T=0$ to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a verity of accurate exponents for domain wall stiffness and finite-size corrections that allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattices Ising spin glasses.

arXiv comment12 pages, 4 figs, 1 table. Review summarizing several dispersed papers with improved figures, published version. Related information can be found at https://physics.emory.edu/faculty/boettcher/

References in corpus (32)

• Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
• Optimization with Extremal Dynamics
• Nature of the Spin Glass State
• Aging, rejuvenation and memory : the example of spin glasses
• Spin and link overlaps in 3-dimensional spin glasses
• Lower Critical Dimension of Ising Spin Glasses
• Energy exponents and corrections to scaling in Ising spin glasses
• Extremal Optimization for Sherrington-Kirkpatrick Spin Glasses
• Stiffness of the Edwards-Anderson Model in all Dimensions
• Critical Percolation in High Dimensions
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• Large Deviations in the Free-Energy of Mean-Field Spin-Glasses
• Finite size corrections in the Sherrington-Kirkpatrick model
• Ground-state clusters of two-, three- and four-dimensional +-J Ising spin glasses
• Interface energies in Ising spin glasses
• Stiffness Exponents for Lattice Spin Glasses in Dimensions d=3,...,6
• Low-Temperature Excitations of Dilute Lattice Spin Glasses
• Conjecture on the maximum cut and bisection width in random regular graphs
• Numerical Results for Ground States of Spin Glasses on Bethe Lattices
• Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field
• Simulations of Ground State Fluctuations in Mean-Field Ising Spin Glasses
• Low Energy Excitations in Spin Glasses from Exact Ground States
• The Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions
• Reduction of Spin Glasses applied to the Migdal-Kadanoff Hierarchical Lattice
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Analysis of the Relation between Quadratic Unconstrained Binary Optimization (QUBO) and the Spin Glass Ground-State Problem
• Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings
• Ground State Properties of the Diluted Sherrington-Kirkpatrick Spin Glass
• Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions
• Deep reinforced learning heuristic tested on spin-glass ground states: The larger picture
• Finite-Size Corrections for Ground States of Edwards-Anderson Spin Glasses
• Reduction of Dilute Ising Spin Glasses

Cited by in corpus (2)

• Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
• Nature of spin glass order in physical dimensions