Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

Fernández, L. A.; Martı́n-Mayor, V.; Pérez-Gaviro, S.; Tarancón, A.; Young, A. P.

doi:10.1103/physrevb.80.024422

Cited by 90 publications

(175 citation statements)

References 25 publications

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“…In the light of the nonself-averaging behavior reported above for the ISG models, it is clear that the published spin and chiral nonself-averaging data [29][30][31] in 3D Heisenberg and XY models are incompatible with a spin-driven ordering scenario [23][24][25][26][27] but strongly support the alternative conclusion that the spin glass ordering in these models is chiral-driven rather than spin-driven, on the Kawamura scenario [28]. An important implication is that order in the canonical experimental Heisenberg spin glasses is also chirality driven.…”

Section: Discussionmentioning

confidence: 99%

“…The numerical simulations in the spin glasses are even more demanding than in the fully frustrated models, and because of intrinsic finite size corrections and the need to reach strict equilibration at each L, extrapolations to infinite L in order to estimate the ThL crossing point locations are delicate. As simulations were extended to larger sizes in successive Gaussian HSG and XYSG measurements interpreted on the spin-driven ordering scenario, the joint spin/chiral crossover temperature was estimated to be T c (HSG) ≈ 0.160 [23], T c (HSG) ≈ 0.145 with a KTB-like critical line [24], marginal but very similar spin and chiral behavior (XYSG and HSG) [25,26], and most recently T c (HSG) ≈ 0.120 [27]. No non-self-averaging results were reported.…”

Section: Heisenberg and Xy Spin Glassesmentioning

confidence: 99%

“…According to the first interpretation, the ordering is spin-spin interaction driven; basically the ordering process is much the same as in ISGs, and the chiral order follows on as a geometrically necessary consequence of the onset of spin order, without the chiral interactions playing any significant role in the spin glass transition [23][24][25][26][27]. The alternative interpretation is that the driving role in 3D HSG or XYSG ordering is played by the chirality, so that there is first a chiral order onset followed at a lower temperature by spin ordering transition [28][29][30][31].…”

Section: Heisenberg and Xy Spin Glassesmentioning

confidence: 99%

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Non-self-averaging in Ising spin glasses and hyperuniversality

Lundow¹,

Campbell²

2016

Phys. Rev. E

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Ising spin glasses with bimodal and Gaussian near-neighbor interaction distributions are studied through numerical simulations. The non-self-averaging (normalized inter-sample variance) parameter U22(T, L) for the spin glass susceptibility (and for higher moments Unn(T, L)) is reported for dimensions 2, 3, 4, 5 and 7. In each dimension d the non-self-averaging parameters in the paramagnetic regime vary with the sample size L and the correlation lengthand so follow a renormalization group law due to Aharony and Harris [1]. Empirically, it is found that the K d values are independent of d to within the statistics. The maximum values [Unn(T, L)]max are almost independent of L in each dimension, and remarkably the estimated thermodynamic limit critical [Unn(T, L)]max peak values are also dimension-independent to within the statistics and so are "hyperuniversal". These results show that the form of the spin-spin correlation function distribution at criticality in the large L limit is independent of dimension within the ISG family. Inspection of published non-self-averaging data for 3D Heisenberg and XY spin glasses the light of the Ising spin glass non-self-averaging results show behavior incompatible with a spin-driven ordering scenario, but compatible with that expected on a chiral-driven ordering interpretation.

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Section: Discussionmentioning

confidence: 99%

Section: Heisenberg and Xy Spin Glassesmentioning

confidence: 99%

Section: Heisenberg and Xy Spin Glassesmentioning

confidence: 99%

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Non-self-averaging in Ising spin glasses and hyperuniversality

Lundow¹,

Campbell²

2016

Phys. Rev. E

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“…10, that we briefly recall. Let β (i) (t) be the inverse temperature of the system i at time t (i = 0, .…”

mentioning

confidence: 99%

Critical behavior of three-dimensional disordered Potts models with many states

Baños¹,

Cruz²,

Fernández³

et al. 2010

J. Stat. Mech.

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We study the 3D Disordered Potts Model with p = 5 and p = 6. Our numerical simulations (that severely slow down for increasing p) detect a very clear spin glass phase transition. We evaluate the critical exponents and the critical value of the temperature, and we use known results at lower p values to discuss how they evolve for increasing p. We do not find any sign of the presence of a transition to a ferromagnetic regime.

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“…One of the most important and unsolved problems in spin-glass studies is the coupling or separation of the spin-glass (sg) degrees of freedom and chiral-glass (cg) degrees of freedom [18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41]. Kawamura [25,26] introduced the chirality scenario, wherein the cg order exists without the sg order.…”

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confidence: 99%

From measurements to inferences of physical quantities in numerical simulations

Nakamura

2016

Phys. Rev. E

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We propose a change of style for numerical estimations of physical quantities from measurements to inferences. We estimate the most probable quantities for all the parameter region simultaneously by using the raw data cooperatively. Estimations with higher precisions are made possible. We can obtain a physical quantity as a continuous function, which is differentiated to obtain another quantity. We applied the method to the Heisenberg spin-glass model in three dimensions. A dynamic correlation-length scaling analysis suggests that the spin-glass and the chiral-glass transitions occur at the same temperature with a common exponent ν. The value is consistent with the experimental results. We found that a size-crossover effect explains a spin-chirality separation problem.Introduction-Estimations of physical quantities in numerical simulations are based on equilibrium statistical physics [1]. We virtualize a model system in a computer and perform independent measurements on the system using a definition of a physical quantity. When an evaluation process is complex, both systematic and statistical errors are accumulated in the obtained data. We sometimes encounter numerical instabilities, which may affect a final physical conclusion. In what follows, we explain the situation of interest using a correlation-length estimation.An estimation formula for a correlation length, ξ, is given by the second-moment method:. Here, χ 0 denotes the susceptibility and χ k its Fourier transform with k as the lowest wave number of the system. This expression itself is problematic. Both numerator and denominator of this expression approach zero as the system size increases (k → 0), where this formula becomes exact. We encounter the numerical instability caused by the expression 0/0. In order to avoid this problem, Bellettiet al. [3] proposed the reduction of this instability by estimating ξ through the integrals I k = 0 drr k f (r) and ξ is obtained as I 2 /I 1 . Suwa and Todo [4] proposed a generalized moment method for gap (∆ ∼ 1/ξ) estimation in quantum systems. Systematic errors and ambiguity caused by using small-L data are eliminated.Recently, big-data handling has become possible due to rapid increase in computational power. Data science is now one of the most promising fields in science and technology. As regards its application to physics, the topic of Bayesian inference has attracted considerable interest [5,6]. In this context, Harada [7] introduced Bayesian inference into a parameter estimation of the finite-size scaling analysis.In this paper, we extend its application to estimations of physical quantities. For example, we can obtain an analytic expression for an energy out of the discrete raw data as the most-probable model function. Then, we obtain the specific heat by analytically differentiating it. A critical temperture is estimated automatically within this procedure. Since directly-observed (raw) data are

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Phase transition in the three dimensional Heisenberg spin glass: Finite-size scaling analysis

Cited by 90 publications

References 25 publications

Non-self-averaging in Ising spin glasses and hyperuniversality

Non-self-averaging in Ising spin glasses and hyperuniversality

Critical behavior of three-dimensional disordered Potts models with many states

From measurements to inferences of physical quantities in numerical simulations

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