3D spin glass and 2D ferromagnetic<b><i>XY</i></b>model: a comparison

Íñiguez, D.; Marinari, Enzo; Parisi, Giorgio; Ruiz‐Lorenzo, J. J.

doi:10.1088/0305-4470/30/21/010

Cited by 25 publications

(34 citation statements)

References 20 publications

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“…1c converges to Fig. 1a or While some simulations appear to support infinite degeneracy [15,16,17], others do not [18,19,20,21,22], and a recent analytic treatment argues against it [23,24]. We note that the droplet picture is a theory concerning the zero-temperature fixed point, while most studies suggesting the validity of the mean-field picture are based on numerical estimates of P (0) at T only as low as 0.7T c , where the glass transition temperature T c is approximately 1.0.…”

Section: Introductionsupporting

confidence: 55%

Evidence for the double degeneracy of the ground state in the three-dimensional±Jspin glass

Hatano

Gubernatis

2002

Phys. Rev. B

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A bivariate version of the multicanonical Monte Carlo method and its application to the simulation of the three-dimensional ±J Ising spin glass are described. We found the autocorrelation time associated with this particular multicanonical method was approximately proportional to the system volume, which is a great improvement over previous methods applied to spin-glass simulations.The principal advantage of this version of the multicanonical method, however, was its ability to access information predictive of low-temperature behavior. At low temperatures we found results on the three-dimensional ±J Ising spin glass consistent with a double degeneracy of the groundstate: the order-parameter distribution function P (q) converged to two delta-function peaks and the Binder parameter approached unity as the system size was increased. With the same density of states used to compute these properties at low temperature, we found their behavior changing as the temperature is increased towards the spin glass transition temperature. Just below this temperature, the behavior is consistent with the standard mean-field picture that has an infinitely degenerate ground state. Using the concept of zero-energy droplets, we also discuss the structure of the ground-state degeneracy. The size distribution of the zero-energy droplets was found to produce the two delta-function peaks of P (q).

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Section: Introductionsupporting

confidence: 55%

Evidence for the double degeneracy of the ground state in the three-dimensional±Jspin glass

Hatano

Gubernatis

2002

Phys. Rev. B

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“…Notice, that for the two-dimensional XY model, /L and the Binder cumulant behave in the same way as L and T. 10 This is an interesting point to compare the behavior of the g 4 and G cumulants, defined above, with /L. From Fig.…”

Section: Numerical Resultsmentioning

confidence: 79%

“…5 On the other hand, the theoretical approach is almost limited to the Monte Carlo simulation of the Edwards-Anderson model, given the enormous difficulties found when using field-theoretic renormalization group techniques. 6 Recent numerical simulations [7][8][9][10][11] have found indications of a finitetemperature phase transition, which has been confirmed in Ref. 12.…”

Section: Introductionmentioning

confidence: 61%

“…͑18͒ are displayed in Table II. Finite-size scaling corrections cannot be resolved within errors, especially if one realizes that the results for the (5,10) pair are anticorrelated with the results for the (10,20) pair ͓the measure in Lϭ10 appears once in the numerator and the other time in the denominator of Eq. ͑18͔͒.…”

Section: Numerical Resultsmentioning

confidence: 98%

“…However, the possibility 10 of a Kosterlitz-Thoulesslike phase transition ͑an exponential divergence of the correlation length at the critical temperature followed by a line of critical points͒ could not be excluded. 12 Even so, criticalexponent estimates that could be compared with experiments were obtained [7][8][9][10][11][12][13][14][15] by assuming power-law divergences at the critical temperature ͑i.e., non-Kosterlitz-Thouless behavior͒. However, the statistical errors of those estimates ͑10% for the correlation-length exponent and 15% in the anomalous dimension ) and that of the critical temperature estimate seem poor compared to similar computations for ordered systems, which is due to the numerical difficulties encountered in the simulation of the Edwards-Anderson model.…”

Section: Introductionmentioning

confidence: 99%

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Critical behavior of the three-dimensional Ising spin glass

et al. 2000

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We have simulated, using parallel tempering, the three-dimensional Ising spin glass model with binary couplings in a helicoidal geometry. The largest lattice (Lϭ20) has been studied using a dedicated computer ͑the SUE machine͒. We have obtained, measuring the correlation length in the critical region, strong evidence for a second-order finite-temperature phase transition, ruling out other possible scenarios like a KosterlitzThouless phase transition. Precise values for the and critical exponents are also presented.

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Exploring Quantum Annealing Architectures: A Spin Glass Perspective

Jaumà,

García‐Ripoll,

Pino

2024

Adv Quantum Tech

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This work analyzes the spin‐glass transition across various Ising models relevant to quantum annealers. By employing the parallel tempering method, the location of the spin‐glass phase transition is extrapolated from the pseudo‐critical temperature of finite‐sized systems. The results confirm a spin‐glass phase at finite temperature in random‐regular and small‐world graphs, in agreement with previous studies. However, strong evidence is obtained that this phase only occurs at zero temperature in the quasi‐2D graphs of D‐Wave, as their pseudo‐critical temperature drifts toward zero. This implies that the asymptotic runtime to find the low‐energy configuration of those graphs is likely to be polynomial in the size of the problem. Nevertheless, this scaling may only be reached for system sizes much larger than existing annealers, as the drift in the pseudo‐critical temperature is slow. This slowness, together with an abrupt increase in thermalization times around the pseudo‐critical temperature, may render the search for low‐energy configurations with classical methods impractical.

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3D spin glass and 2D ferromagneticXYmodel: a comparison

Cited by 25 publications

References 20 publications

Evidence for the double degeneracy of the ground state in the three-dimensional±Jspin glass

Evidence for the double degeneracy of the ground state in the three-dimensional±Jspin glass

Critical behavior of the three-dimensional Ising spin glass

Exploring Quantum Annealing Architectures: A Spin Glass Perspective

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