Ground-state topology of the Edwards-Anderson +/-J spin glass model

Abstract

In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.

arXiv comment16 pages and 21 figures

References in corpus (21)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Precise determination of the bond percolation thresholds and finite-size scaling corrections for the s.c., f.c.c., and b.c.c. lattices
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Fluctuation-dissipation ratio of a spin glass in the aging regime
• Monte-Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes
• Lower Critical Dimension of Ising Spin Glasses
• On the freezing of variables in random constraint satisfaction problems
• Scaling of stiffness energy for 3d +/-J Ising spin glasses
• Measuring the fluctuation-dissipation ratio in glassy systems with no perturbing field
• Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions
• On Mean Field Glassy Dynamics out of Equilibrium
• Ground-state behavior of the 3d +/-J random-bond Ising model
• Glassy dynamics near zero temperature
• The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm
• Exact Algorithm for Sampling the 2D Ising Spin Glass
• Signature of the Ground-State Topology in the Low-Temperature Dynamics of Spin Glasses
• Influence of the Ground-State Topology on the Domain-Wall Energy in the Edwards-Anderson +/- J Spin Glass Model
• Strong Dynamical Heterogeneities in the Violation of the Fluctuation-Dissipation Theorem in Spin Glasses
• Domain growth within the backbone of the three-dimensional $\pm J$ Edwards-Anderson spin glass

Cited by in corpus (10)

• Zero and low temperature behavior of the two-dimensional $\pm J$ Ising spin glass
• Chaos and universality in two-dimensional Ising spin glasses
• Interplay of Topological Order and Spin Glassiness in the Toric Code under Random Magnetic Fields
• Domain-wall excitations in the two-dimensional Ising spin glass
• Dual time scales in simulated annealing of a two-dimensional Ising spin glass
• Elementary excitations and the phase transition in the bimodal Ising spin glass model
• Backbone structure of the Edwards-Anderson spin-glass model
• Dynamical heterogeneities as fingerprints of a backbone structure in Potts models
• Nonequilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with Gaussian couplings: Strong heterogeneities and the backbone picture
• Changing the universality class of the three-dimensional Edwards-Anderson spin-glass model by selective bond dilution