Novel order parameter to describe the critical behavior of Ising spin glass models

Romá, F.; Nieto, F.; Ramírez-Pastor, A. J.; Vogel, E.E.

doi:10.1016/j.physa.2005.08.052

Cited by 10 publications

(14 citation statements)

References 31 publications

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“…They found that the fraction of solidary spins in 3D(2D) is 0.76(0.67) of the total. In contrast with what is observed in 2D [20,21], the largest component of the solidary spins in 3D does not fragment as the system size grows, involving 60% of all the spins. Furthermore, the largest component in 3D forms a compact percolating cluster [22].…”

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confidence: 83%

“…This structure can be used to divide the spins in the system in two sets: solidary spins, which are the spins in the backbone and thus maintain their relative orientation in all the ground-state configurations, and non-solidary spins which are simply all the spins that are not in the backbone [11]. Further insight in the static properties of the 3D and 2D EA model has been recently addressed by Romá et al [21,22]. They found that the fraction of solidary spins in 3D(2D) is 0.76(0.67) of the total.…”

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Strong Dynamical Heterogeneities in the Violation of the Fluctuation-Dissipation Theorem in Spin Glasses

et al. 2007

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We analyze numerically the violation of the fluctuation-dissipation theorem (FDT) in the ±J EdwardsAnderson (EA) spin glass model. Using single spin probability densities we reveal the presence of strong dynamical heterogeneities, which correlate with ground state information. The physical interpretation of the results shows that the spins in the EA model can be divided in two sets. In 3D, one set forms a compact structure which presents a coarsening-like behavior with its characteristic violation of the FDT, while the other asymptotically follows the FDT. Finally, we compare the dynamical behavior observed in 3D with 2D. PACS numbers: 75.10.Nr, 75.40.Gb, 75.40.Mg The study of glassy behavior, characterized by out-ofequilibrium dynamics that present very long relaxation times, involves a vast range of different systems such as spin glasses [1], structural glasses, colloidal and polymeric systems, and granular systems to name just a few [2]. These systems present out-of-equilibrium properties such as aging and violation of the fluctuation-dissipation theorem (FDT) [3,4], whose characterization can be used as signatures of typical dynamical behaviors. For example, according to their deviation from the FDT they can be classified into three different groups: coarsening, structural glass and spin glass systems [3]. These cases have been theoretically described in terms of replica-symmetry breaking (RSB): in coarsening systems replica symmetry is unbroken, structural glasses correspond to one-step RSB and spin glasses to full RSB [3]. In the case of short-range spin glasses, most results on the violation of the FDT have been qualitatively and quantitatively described in the framework of mean field theory (full RSB) [3,5]. Also direct experimental evidence on the violation of the FDT in an insulating spin glass [6] have been fitted by mean field theory.In this work we show that, in contrast to these results, the violation of the FDT in the 3D ±J Edwards-Anderson (EA) model is the result of two components with completely different behaviors: one that tends to satisfy the FDT relation, and another which presents a violation of this relation similar to coarsening systems. The behavior of the latter component seems to be compatible with the droplet picture scenario [7].We reveal the presence of two components in the violation of the FDT by a careful analysis of dynamical heterogeneities. In principle, two different approaches may be used to study the development of dynamical heterogeneities. On one hand, it is possible to use space or time coarse-grained protocols [8,9]. On the other hand, it is possible to use single spin observables looking for a direct observation of the local heterogeneities. In any of these approaches, if one is interested in making disorder averages and chooses to identify the spins by their position in the lattice, trivial results are obtained, since the difference between spins are washed out [10]. Here we take a local approach, but in contrast with previous works, we properly include disorder a...

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Strong Dynamical Heterogeneities in the Violation of the Fluctuation-Dissipation Theorem in Spin Glasses

et al. 2007

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“…It is worth stressing that usually one is interested in studying the outof-equilibrium properties below the critical temperature T c . However, in the two-dimensional EA spin glass model T c 0 [21,22]. Nevertheless, it is widely accepted that for low enough temperatures, the dynamics remains out of equilibrium at short times and is very similar to the one observed in three-dimensional spin glasses [12,23].…”

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Signature of the Ground-State Topology in the Low-Temperature Dynamics of Spin Glasses

Romá

Bustingorry

2006

Phys. Rev. Lett.

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We numerically address the issue of how the ground-state topology is reflected in the finite temperature dynamics of the +/-J Edwards-Anderson spin glass model. In this system a careful study of the ground-state configurations allows us to classify spins into two sets: solidary and nonsolidary spins. We show that these sets quantitatively account for the dynamical heterogeneities found in the mean flipping time distribution at finite low temperatures. The results highlight the relevance of taking into account the ground-state topology in the analysis of the finite temperature dynamics of spin glasses.

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“…20,21 Using a parallel tempering Monte Carlo algorithm it is possible to systematically arrive at GS configurations, 22 which are necessary to determine the rigid lattice. We stress that the determination of this structure for each disorder realization requires to visit O͑N͒ times the GS.…”

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

2010

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The goal of this work is to show that a ferromagneticlike domain-growth process takes place within the backbone of the three-dimensional ϮJ Edwards-Anderson ͑EA͒ spin glass model. To sustain this affirmation we study the heterogeneities displayed in the out-of-equilibrium dynamics of the model. We show that both correlation function and mean flipping time distribution present features that have a direct relation with spatial heterogeneities, and that they can be characterized by the backbone structure. In order to gain intuition we analyze the pure ferromagnetic Ising model, where we show the presence of dynamical heterogeneities in the mean flipping time distribution that are directly associated to ferromagnetic growing domains. We extend a method devised to detect domain walls in the Ising model to carry out a similar analysis in the threedimensional EA spin-glass model. This allows us to show that there exists a domain-growth process within the backbone of this model.

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Novel order parameter to describe the critical behavior of Ising spin glass models

Cited by 10 publications

References 31 publications

Strong Dynamical Heterogeneities in the Violation of the Fluctuation-Dissipation Theorem in Spin Glasses

Strong Dynamical Heterogeneities in the Violation of the Fluctuation-Dissipation Theorem in Spin Glasses

Signature of the Ground-State Topology in the Low-Temperature Dynamics of Spin Glasses

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

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