Damage spreading and ferromagnetic order in the three-dimensional ±J Edwards-Anderson spin glass model

Abstract

Using information of the ground-state topology we show that the damage spreading technique unveils ferromagnetic order in the three-dimensional ±J Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than Tg, the glass transition temperature. With spin-orienting dynamics and for temperatures in Tg < T < T d , damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. T d is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, Tc. The present results allow for an interpretation within a single framework of known -and sometimes puzzling-results, giving an intuitive picture for growing order in spin glasses.

Domain growth within the backbone of the three-dimensional±JEdwards-Anderson spin glass

“…All these results, together with other recent works that show the relevance of the heterogeneous character of the GS topology, [14][15][16]28 point to an alternative picture for the nature of the spin-glass phase. Within this picture, ferromagneticlike order grows within a constrained structure of the system.…”

“…The results suggest that a domaingrowth process might be present within the backbone while those spins outside the backbone tend to equilibrium behavior. 15 Also, by using the damage-spreading technique, we have results showing that ferromagneticlike order grows in the 3D ϮJ EA model below the pure ferromagnetic critical temperature T c , pointing to the presence of a Griffithslike phase in the range T g Ͻ T Ͻ T c , 16 where T g is the glass transition temperature. Again, these results are suggestive of a domain-growth process inside the backbone structure.…”

“…12,13 We have recently incorporated this spatial heterogeneous character of the GS into the analysis of dynamical heterogeneities present in the out-ofequilibrium dynamics 14,15 and also in the study of equilibrium properties of the system. 16 In Ref. 14 we have analyzed the two-dimensional EA model and we have correlated the presence of slow and fast sets of spins with the backbone structure.…”

Backbone structure of the Edwards-Anderson spin-glass model

“…More specifically, the backbone and its complement seem to influence both the equilibrium and the out-of-equilibrium dynamics of the EAB models [11,[13][14][15][16][17]. Here we have shown that in systems with continuous distributions of bonds it is possible to define a continuous version of bond rigidity, which in turn leads to the definition of a backbone.…”

“…Recently, a new approach [11][12][13][14][15][16][17] has been put forward that can provide a new way to reinterpret some of the numerical and theoretical data in the literature. Based on the same spirit as the droplet picture, which focuses on the ground state (GS) and its excitations, in this approach the spatial heterogeneities of the GS play a fundamental role in describing the low-temperature behavior of the system.…”