Backbone structure of the Edwards-Anderson spin-glass model

Abstract

We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.

Nonequilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with Gaussian couplings: strong heterogeneities and the backbone picture

“…In fact, as shown in Ref. [27], in 2D a rigidity threshold value r min can be found to separate the system into highrigidity (HR) and low-rigidity (LR) components such that the EAB and the EAG models share the same percolation properties and have a similar equilibrium behavior.…”

“…These studies have resulted in a generalization of the cluster approach for spin glasses (and for other systems with quenched disorder), appropriately named the "backbone picture" [24,27]. The main conjecture of this picture is that it is possible to define an "effective interaction" between a pair of spins at sites i and j, different from the bond strength J ij .…”

“…This can be accessed for spin-glass models with Ising spin variables [24,27], based on the ground-state configurations and the low-excitation levels. In particular, in Ref.…”

“…In Ref. [27], a parallel tempering Monte Carlo algorithm [40,41] was used for this purpose. This technique, widely used in equilibrium simulations, also provides a powerful heuristic method for reaching the GS of spin-glass models [42,43].…”

“…In particular, for the 3D EAG model, the parallel tempering algorithm allows one to obtain GSs with a high probability for lattice sizes up to L = 10 [43]. Since 3N of such configurations are required to calculate the RS of a single sample, we restrict our analysis to L = 8 [27]. The interpretation of the rigidity r ij as an effective interaction is the basis on which rests a generalized definition of the backbone.…”