The ground state energy of the Edwards–Anderson spin glass model with a parallel tempering Monte Carlo algorithm

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

doi:10.1016/j.physa.2009.03.036

Cited by 27 publications

(71 citation statements)

References 42 publications

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“…It is well known that finding the GS of spin glass system in D = 3 is an NP-complete problem [59,60] and there exist a large number of heuristic algorithms developed in order to tackle this outstanding problem [60][61][62][63][64]. In a recent paper, Roma et al [37] have concluded that PT is comparable to the performance of the more powerful heuristics. In particular, they have concentrated on the estimation of the minimum number of PTSs needed to achieve a true GS with a given probability.…”

Section: Ground States Of 3d Spin-glass Modelsmentioning

confidence: 99%

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Comparative study of selected parallel tempering methods

Malakis

Papakonstantinou²

2013

Phys. Rev. E

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We review several parallel tempering schemes and examine their main ingredients for accuracy and efficiency. The present study covers two selection methods of temperatures and several choices for the exchange of replicas, including a recent novel all-pair exchange method. We compare the resulting schemes and measure specific heat errors and efficiency using the two-dimensional (2D) Ising model. Our tests suggest that, an earlier proposal for using numbers of local moves related to the canonical correlation times is one of the key ingredients for increasing efficiency, and protocols using cluster algorithms are found to be very effective. Some of the protocols are also tested for efficiency and ground state production in 3D spin glass models where we find that, a simple nearestneighbor approach using a local n-fold way algorithm is the most effective. Finally, we present evidence that the asymptotic limits of the ground state energy for the isotropic case and that of an anisotropic case of the 3D spin-glass model are very close and may even coincide.

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Section: Ground States Of 3d Spin-glass Modelsmentioning

confidence: 99%

“…We note that, due to some differences in defining the PTS, our notation is not identical with that in Ref. [37], but the analogies are obvious and we will also use N s to denote the number of different samples. The collapse example in Fig.…”

Section: A Ground States Of the 3d Eab Model: Further Tests Of Pt Prmentioning

confidence: 99%

Comparative study of selected parallel tempering methods

Malakis

Papakonstantinou²

2013

Phys. Rev. E

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“…17,18 Recently, we have shown that this technique is a powerful heuristic method for reaching the GS of the EAB model up to L = 30 in 2D and L = 14 in 3D. 19 As in the RLSA many independent runs of parallel tempering are needed, we have obtained the RL of samples up to L = 18 in 2D and L = 9 in 3D. Parameters used here are the same as in Ref.…”

Section: Model and Algorithmmentioning

confidence: 99%

“…Parameters used here are the same as in Ref. 19 and n = 10 independent runs were carried out in all the cases.…”

Section: Model and Algorithmmentioning

confidence: 99%

Ground-state topology of the Edwards-Anderson±Jspin glass model

et al. 2010

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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.

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“…For the systems with (J 1 , J 2 ) couplings and vacancies, sufficiently large system sizes are required in order to find the true groundstate among numerous possible magnetic configurations. For this purpose, the parallel tempering technique based on Monte Carlo method, which was applied in studying spin glass systems [48], is an appropriate approach. Once the groundstate is determined, the magnetic order-disorder phase transition at finite temperatures can be investigated by large-scale Monte Carlo simulations.…”

Section: Introductionmentioning

confidence: 99%