Lower Critical Dimension of Metallic Vector Spin-Glasses

Aj, Bray; Moore, M. A.; Ap, Young

doi:10.1103/physrevlett.56.2641

Cited by 138 publications

(105 citation statements)

References 22 publications

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“…The interpretation proposed in [28] is that Eq. 7 is nevertheless exact in the whole region 1 2 < σ < 2 as predicted by the theoretical derivations [23,25], and despite their numerical results [28] . Another interpretation could be that the saturation seen in the numerics is meaningful, and that Eq.…”

Section: A Gaussian Distributionmentioning

confidence: 83%

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One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Monthus¹

2014

J. Stat. Mech.

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For the one-dimensional long-ranged Ising spin-glass with random couplings decaying with the distance r as J(r) ∼ r −σ and distributed with the Lévy symmetric stable distribution of index 1 < µ ≤ 2 (including the usual Gaussian case µ = 2), we consider the region σ > 1/µ where the energy is extensive. We study two real space renormalization procedures at zero temperature, namely a simple box decimation that leads to explicit calculations, and a strong disorder decimation that can be studied numerically on large sizes. The droplet exponent governing the scaling of the renormalized couplings JL ∝ L θµ(σ) is found to be θµ(σ) = 2 µ −σ whenever the long-ranged couplings are relevant θµ(σ) ≥ −1. For the statistics of the ground state energy E GS L over disordered samples, we obtain that the droplet exponent θµ(σ) governs the leading correction to extensivity of the averaged value E GS L ≃ Le0 + L θµ (σ) e1. The characteristic scale of the fluctuations around this average is of order L 1 µ , and the rescaledGaussian distributed for µ = 2, or displays the negative power-law tail in 1/(−u) 1+µ for u → −∞ in the Lévy case 1 < µ < 2. Finally we apply the zero-temperature renormalization procedure to the related Dyson hierarchical spin-glass model where the same droplet exponent appears.

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Section: A Gaussian Distributionmentioning

confidence: 83%

“…The corresponding droplet exponent θ LR (d, σ) is then believed to be known exactly [23,25] in the region of parameters where it is bigger than the corresponding short-ranged droplet exponent θ SR (d)…”

Section: Introductionmentioning

confidence: 99%

One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Monthus¹

2014

J. Stat. Mech.

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“…The Hamiltonian of the one-dimensional long-range Ising spin glass with random power-law interactions 16,17 is given by…”

Section: Model Observables and Numerical Detailsmentioning

confidence: 99%

Probing the Almeida-Thouless line away from the mean-field model

2005

Self Cite

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Results of Monte Carlo simulations of the one-dimensional long-range Ising spin glass with powerlaw interactions in the presence of a (random) field are presented. By tuning the exponent of the power-law interactions, we are able to scan the full range of possible behaviors from the infiniterange (Sherrington-Kirkpatrick) model to the short-range model. A finite-size scaling analysis of the correlation length indicates that the Almeida-Thouless line does not occur in the region with non-mean-field critical behavior in zero field. However, there is evidence that an Almeida-Thouless line does occur in the mean-field region.

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“…The second study [10] predicts that a site-diluted BCC lattice is ferromagnetically ordered above x=0.21 with a spin-glass phase below x=0.21. It is also interesting to note that a study of the three dimensional RKKY Ising spin glass, with an interaction of mixed sign proportional to 1/r 3 , finds that this system lies on the boundary between a finite temperature and a T c = 0 spin glass [11].…”

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confidence: 99%

Phase diagram of the dilute magnetLiHoxY1−xF4

Biltmo

Henelius

2007

Phys. Rev. B

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We study the effective long-range Ising dipole model with a local exchange interaction appropriate for the dilute magnetic compound LiHoxY1−xF4. Our calculations yield a value of 0.12 K for the nearest neighbor exchange interaction. Using a Monte Carlo method we calculate the phase boundary Tc(x) between the ferromagnetic and paramagnetic phases. We demonstrate that the experimentally observed linear decrease in Tc with dilution is not the simple mean-field result, but a combination of the effects of fluctuations, the exchange interaction and the hyperfine coupling. Furthermore, we find a critical dilution xc = 0.21(2), below which there is no ordering. In agreement with recent Monte Carlo simulations on a similar model, we find no evidence of the experimentally observed freezing of the glassy state in our calculation. We apply the theory of Stephen and Aharony to LiHoxY1−xF4 and find that the theory does predict a finite-temperature freezing of the spin glass. Reasons for the discrepancies are discussed. The rare-earth compound LiHo x Y 1−x F 4 has been widely used as a model magnet displaying a wide range of phenomena. At T c =1.53 K the predominant longrange dipolar interaction causes a second order classical phase transition to a ferromagnetic state [1]. By applying a transverse magnetic field the order can be destroyed in a T=0 quantum phase transition at about 4.9 T[2]. Positional disorder can be introduced by substituting the magnetic Ho 3+ ions with non-magnetic Y 3+ ions. The disorder has been shown to cause a transition to glassy behavior at high dilution [3].A main attraction of LiHo x Y 1−x F 4 is that the microscopic model is well-known [3,4]. The ground state of the Ho 3+ ion in the crystal field is an Ising doublet, with the first excited state 11 K above the ground state. At the temperature range we consider here (T < 1.5 K) LiHoF 4 should be a very good realization of a dipolar Ising modelwhere J is the dipolar coupling constant, J ex the nearestneighbor exchange constant, r ij the interspin distance and z ij the interspin distance along the Ising axis. The summation is done over all Ho 3+ ions, which form a tetragonal Bravais lattice with four ions per unit cell. When diluted, a fraction x of the sites are occupied by non-magnetic Yttrium and not included in the above sum. The size of the unit cell is (1, 1, 2.077) in units of a = 5.175Å. If we express the interspin distance in units of a, then the dipolar coupling constant J = (gµ B /2) 2 /a 3 = 0.214K [4]. The exchange coupling J ex has been experimentally determined to about half of the nearest-neighbor dipolar coupling [5]. In our calculation we have neglected the next nearest neighbor exchange interaction, which was found to be about 5% of the nearestneighbor dipolar coupling [5]. In addition, we have left out the hyperfine coupling between the nuclear and electronic spins as well as the random fields generated by the breaking of crystal symmetries due to the dilution. The effects of these terms on our results will be discussed.

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Lower Critical Dimension of Metallic Vector Spin-Glasses

Cited by 138 publications

References 22 publications

One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

One-dimensional Ising spin-glass with power-law interaction: real-space renormalization at zero temperature

Probing the Almeida-Thouless line away from the mean-field model

Phase diagram of the dilute magnetLiHoxY1−xF4

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