Frozen quasi-long-range order in the random anisotropy Heisenberg magnet

Itakura, Mitsuhiro

doi:10.1103/physrevb.68.100405

Cited by 46 publications

(58 citation statements)

References 25 publications

(38 reference statements)

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“…17 In three dimensions, instead, the phase diagram has been controversial for a long time. While for small values of D numerical simulations 5,[18][19][20][21][22] confirmed the existence of a finitetemperature transition ͑though QLRO was never observed͒, in the SRAM even the existence of the transition was in doubt. 21 In Ref.…”

Section: Introductionmentioning

confidence: 95%

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Liers¹,

Lukic²,

Marinari³

et al. 2007

Phys. Rev. B

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We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find theta=-0.275(5) and theta approximate to 0.2, respectively, in two and three dimensions. These results strongly suggest that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions, our data strongly support the absence of spontaneous magnetization in the infinite-volume limit

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Section: Introductionmentioning

confidence: 95%

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Liers¹,

Lukic²,

Marinari³

et al. 2007

Phys. Rev. B

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“…We call this configuration the OG-SG state, since it is the combination of the orbital glass (OG) and spin-nematic glass (SG). The OG-SG states produced by random anisotropy of aerogel strands provide the experimental realization of the random anisotropy glasses discussed in different systems [12], such as random anisotropy Heisenberg spin glasses in magnets [13,14] and nematic glasses in liquid crystals [15,16,17].…”

Section: Theorymentioning

confidence: 99%

Orbital glass and spin glass states of 3He-A in aerogel

et al. 2010

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Glass states of superfluid A-like phase of 3 He in aerogel induced by random orientations of aerogel strands are investigated theoretically and experimentally. In anisotropic aerogel with stretching deformation two glass phases are observed. Both phases represent the anisotropic glass of the orbital ferromagnetic vectorl -the orbital glass (OG). The phases differ by the spin structure: the spin nematic vectord can be either in the ordered spin nematic (SN) state or in the disordered spin-glass (SG) state. The first phase (OG-SN) is formed under conventional cooling from normal 3 He. The second phase (OG-SG) is metastable, being obtained by cooling through the superfluid transition temperature, when large enough resonant continuous radio-frequency excitation are applied. NMR signature of different phases allows us to measure the parameter of the global anisotropy of the orbital glass induced by deformation.

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“…(8) and (A8,A9), i.e., for the purely transverse correlation matrix in replica space, G ab,k (q; ρ) → G k (q; ρ; u) G aa,k (q; ρ) → G T,k (q; ρ) + G k (q; ρ) ,…”

Section: Replicon Eigenvaluementioning

confidence: 99%

“…13,14 Furthermore, experiments and simulations have been inconclusive. 6,8,15 We revisit the model by considering its large-N limit. Even this limit has led to controversies, which we clarify and resolve in this work.…”

Section: Introductionmentioning

confidence: 99%

“…[7][8][9] On the other hand, an issue that has not been settled is the existence of a spin-glass phase for strong enough disorder when d > 4 and for any disorder strength when d < 4. Such a phase has been predicted through a variety of theoretical approaches, and sometimes associated with a so-called spontaneous replica-symmetry breaking as in the Sherrington-Kirkpatrick mean-field model of Ising spin glasses, 3,5,[10][11][12] but this result has been challenged.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagram and criticality of the random anisotropy model in the large- N limit

Mouhanna

Tarjus

2016

Phys. Rev. B

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We revisit the thermodynamic behavior of the random-anisotropy O(N ) model by investigating its large-N limit. We focus on the system at zero temperature where the mean-field-like artifacts of the large-N limit are less severe. We analyze the connection between the description in terms of self-consistent Schwinger-Dyson equations and the functional renormalization group. We provide a unified description of the phase diagram and critical behavior of the model and clarify the nature of the possible "glassy" phases. Finally we discuss the implications of our findings for the finite-N and finite-temperature systems.

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Frozen quasi-long-range order in the random anisotropy Heisenberg magnet

Cited by 46 publications

References 25 publications

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

Orbital glass and spin glass states of 3He-A in aerogel

Phase diagram and criticality of the random anisotropy model in the large- N limit

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