Pair correlation function for spin glasses

Fernández, Julio F.; Alonso, Juan J.

doi:10.1103/physrevb.86.140402

Cited by 4 publications

(23 citation statements)

References 45 publications

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“…On the other hand, a direct comparison of our data with MC data obtained for the SK model shows that crucial RSB predictions are also at odds with some of our results. It is noteworthy that the findings enumerated above for DIS are strikingly similar to the ones found in previous MC work for the EA model, [18][19][20]23 though finite size effects have been reported to be strong for the EA model for the available systems sizes in MC simulations.…”

Section: 1939supporting

confidence: 88%

“…We compute the cumulative distribution Π In previous papers 19 we have obtained additional information on the shape and width of spikes from a pair correlation function. (9) and let G Q (q) be the average of G Q J (q) over samples.…”

Section: Measured Quantitiesmentioning

confidence: 99%

“…Qualitatively similar distributions have been observed for the EA and SK models. 18,19,39 It is clear that these inner peaks (that is, peaks away from q ≈ ±1) come from overlaps between states that belong to different basins of attraction. The main aim of this paper is to extract statistical information for these cross-overlap (CO) spikes situated on the interval q ∈ (−Q, Q).…”

Section: A Overlap Distributionsmentioning

confidence: 99%

“…From a suitable defined pair correlation function 19 we compute an averaged width w Q that appears to remain finite as L increases. Complementary to this result, we find that the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. All of this points to finite width for CO spikes in the L → ∞ limit at low temperatures.…”

Section: 1939mentioning

confidence: 99%

“…19 X 2 has been investigated in detail in several papers and it is known to be size independent for both the EA and SK models. …”

mentioning

confidence: 99%

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Low-temperature spin-glass behavior in a diluted dipolar Ising system

Alonso

2015

Phys. Rev. B

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Using Monte Carlo simulations, we study the character of the spin-glass (SG) state of a sitediluted dipolar Ising model. We consider systems of dipoles randomly placed on a fraction x of all L 3 sites of a simple cubic lattice that point up or down along a given crystalline axis. For x 0.65 these systems are known to exhibit an equilibrium spin-glass phase below a temperature Tsg ∝ x. At high dilution and very low temperatures, well deep in the SG phase, we find spiky distributions of the overlap parameter q that are strongly sample-dependent. We focus on spikes associated with large excitations. From cumulative distributions of q and a pair correlation function averaged over several thousands of samples we find that, for the system sizes studied, the average width of spikes, and the fraction of samples with spikes higher than a certain threshold does not vary appreciably with L. This is compared with the behavior found for the Sherrington-Kirkpatrick model.

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Section: 1939supporting

confidence: 88%

Section: Measured Quantitiesmentioning

confidence: 99%

Section: A Overlap Distributionsmentioning

confidence: 99%

Section: 1939mentioning

confidence: 99%

“…19 X 2 has been investigated in detail in several papers and it is known to be size independent for both the EA and SK models. …”

mentioning

confidence: 99%

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Low-temperature spin-glass behavior in a diluted dipolar Ising system

Alonso

2015

Phys. Rev. B

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Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

Alonso¹,

Allés²

2017

J. Phys.: Condens. Matter

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Using tempered Monte Carlo simulations, we study the the spin-glass phase of dense packings of Ising dipoles pointing along random axes. We consider systems of dipoles (i) placed on the sites of a simple cubic lattice with lattice constant d, and (ii) placed at the center of random close packed spheres of diameter d that occupy 64% of the volume. For both cases, we find a spin-glass phase below a certain temperature T . By analysing the data obtained for the overlap parameter, the associated correlation length, as well as the statistics of the overlap distributions of individual samples, we find a behavior consistent with quasi-long-range order in the spin-glass phase, similar to the one previously found in strongly diluted dipolar systems.

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Numerical results for the Edwards-Anderson spin-glass model at low temperature

Fernández

Alonso

2013

Phys. Rev. B

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We have simulated Edwards-Anderson (EA) as well as Sherrington-Kirkpatrick systems of L 3 spins. After averaging over large sets of EA system samples of 3 L 10, we obtain accurate numbers for distributions p(q) of the overlap parameter q at very low-temperature T . We find p(0)/T → 0.233(4) as T → 0. This is in contrast with the droplet scenario of spin glasses. We also study the number of mismatched links-between replica pairs-that come with large scale excitations. Contributions from small scale excitations are discarded. We thus obtain for the fractal dimension of outer surfaces of q ∼ 0 excitations in the EA model d s → 2.59(3) as T → 0. This is in contrast with d s → 3 as T → 0 that is predicted by mean-field theory for the macroscopic limit.

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Pair correlation function for spin glasses

Cited by 4 publications

References 45 publications

Low-temperature spin-glass behavior in a diluted dipolar Ising system

Low-temperature spin-glass behavior in a diluted dipolar Ising system

Nature of the spin-glass phase in dense packings of Ising dipoles with random anisotropy axes

Numerical results for the Edwards-Anderson spin-glass model at low temperature

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