Are ground states of 3d ±
                    <i>J</i>
                    spin glasses ultrametric?

Hartmann, Alexander K.

doi:10.1209/epl/i1998-00464-8

Cited by 22 publications

(17 citation statements)

References 28 publications

(36 reference statements)

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“…The ultrametric solution has passed many numerical tests and it is in agreement with all the known analytical results [6,7]. It is quite possible, and in agreement with the numerical simulations, that the ultrametric organization of the equilibrium configurations is also present in finite dimensional spin glasses [8,9,10,11].…”

Section: Introductionsupporting

confidence: 74%

On the origin of ultrametricity

Parisi

Ricci-Tersenghi

1999

J. Phys. A: Math. Gen.

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In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural assumptions: each replica is equivalent to the others (replica equivalence or stochastic stability) and all the mutual information about a pair of equilibrium configurations is encoded in their mutual distance or overlap (separability or overlap equivalence).

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Section: Introductionsupporting

confidence: 74%

On the origin of ultrametricity

Parisi

Ricci-Tersenghi

1999

J. Phys. A: Math. Gen.

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“…Other numerical simulations done with a different technique in three dimensions on systems with side from 4 to 12 are compatible with ultrametricity, but the approach to zero seems to be much slower that in four dimension and at the present moment it is difficult to reach a definite conclusion [88,89]. This problem should be better investigated in the future.…”

Section: Ultrametricitymentioning

confidence: 71%

Untitled

Marinari

Parisi

Ricci-Tersenghi

et al. 2000

Journal of Statistical Physics

226

278

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We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).

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“…For three dimensional models, most methods for solving zero-temperature problems are based on heuristic optimization since no good exact method is available due to the NP-hardness of the problem. A computation of the ground states of the ±J Ising model up to L = 14 was done 81,82 with a heuristic algorithm called the cluster-exact approximation method. 83 Later the computation was redone, 79,84 in order to fix the problem of the biased sampling.…”

Section: Low-temperature Phase Of the ±J Modelmentioning

confidence: 99%

Recent Progress in Spin Glasses

Kawashima

Rieger

2013

Frustrated Spin Systems

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We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned.The motivation that pulls researchers toward spin glasses is possibly not the potential future use of spin glass materials in "practical" applications. It is rather the expectation that there must be something very fundamental in systems with randomness and frustration. It seems that this expectation has been acquiring a firmer ground as the difficulty of the problem is appreciated more clearly. For example, a close relationship has been established between spin glass problems and a class of optimization problems known to be N P -hard. It is now widely accepted that a good (i.e. polynomial) computational algorithm for solving any one of N P -hard problems most probably does not exist. Therefore, it is quite natural to expect that the Ising spin glass problem, as one of the problem in the class, would be very hard to solve, which indeed turns out to be the case in a vast number of numerical studies. None the less, it is often the case that only numerical studies can decide whether a certain hypothetical picture applies to a given instance. Consequently, the major part of what we present below is inevitably a de-

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Are ground states of 3d ± J spin glasses ultrametric?

Cited by 22 publications

References 28 publications

On the origin of ultrametricity

On the origin of ultrametricity

Untitled

Recent Progress in Spin Glasses

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