Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

Baños, Raúl; Cruz, A.; Fernández, L. A.; Gil-Narvion, J. M.; Gordillo‐Guerrero, A.; Guidetti, M.; Íñiguez, D.; Maiorano, Andrea; Mantovani, Filippo; Marinari, Enzo; Martı́n-Mayor, V.; Monforte-Garcia, J.; Sudupe, A. Muñoz; Navarro, D.; Parisi, Giorgio; Pérez-Gaviro, S.; Ricci-Tersenghi, Federico; Ruiz‐Lorenzo, J. J.; Schifano, Sebastiano Fabio; Seoane, Beatriz; Tarancón, A.; Tripiccione, R.; Yllanes, David

doi:10.1103/physrevb.84.174209

Cited by 24 publications

(24 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…RSB theory extends as well to d < d U features found in the mean field solution [25]: many states (infinitely many in the L → ∞ limit), hierarchically organized, contribute to the Gibbs measure, each one with a weight that depends on the disorder realization. Consequences include the existence of the de Almeida-Thouless line [26] (the spin-glass phase transition survives in the presence of a small external magnetic field [27]), or the strong sample-to-sample fluctuations induced by the nonself-averageness of several measurable quantities [28] (these observations [27,28] were, however, obtained by simulating systems of finite size).…”

mentioning

confidence: 99%

See 1 more Smart Citation

Numerical Construction of the Aizenman-Wehr Metastate

et al. 2017

Self Cite

View full text Add to dashboard Cite

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d ¼ 3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a dispersed metastate, supported on many thermodynamic states.

show abstract

mentioning

confidence: 99%

“…Yet, the main debated points regard the equilibrium metastate. In fact, the only related issue addressed numerically by equilibrium simulations has been nonself-averageness [20,28,[31][32][33].…”

mentioning

confidence: 99%

Numerical Construction of the Aizenman-Wehr Metastate

et al. 2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…20,21 Some have found more useful to study the statistics of the area under p J (q) for q < q m . 17,20 The numerical study of SG models distinct from the SK and EA models has shed some light on the virtues and weaknesses of these new probes for measuring diversity.…”

mentioning

confidence: 99%

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

Alonso

2015

Phys. Rev. B

View full text Add to dashboard Cite

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.

show abstract

“…Quantity X 2 J (Q) J is examined in some detail in Ref. 37, where it is termed X 2 . Now, w(0,Q) and (δp Q ) 2 come into X 2 J (Q) J as a product, which happens to be size independent not only in the EA model then], and [see Eq.…”

mentioning

confidence: 99%

Pair correlation function for spin glasses

Fernández¹,

Alonso²

2012

Phys. Rev. B

View full text Add to dashboard Cite

We extract a pair correlation function (PCF) from probability distributions of the spin-overlap parameter q. The distributions come from Monte Carlo simulations. A measure, w, of the thermal fluctuations of magnetic patterns follows from the PCFs. We also obtain rms deviations (over different system samples) delta_p away from average probabilities for q. For the linear system-sizes $L$ we have studied, (i) w and delta_p are independent of L in the Edwards-Anderson model but scale as 1/L and sqrt{L}, respectively, in the Sherrington-Kirkpatrik model.Comment: 5 LaTex pages, 3 eps figures, 1 table. Submitted to PRL on 13 June, resubmitted to PRB on 17 Jul

show abstract

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

Cited by 24 publications

References 31 publications

Numerical Construction of the Aizenman-Wehr Metastate

Numerical Construction of the Aizenman-Wehr Metastate

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

Pair correlation function for spin glasses

Contact Info

Product

Resources

About