Emergence of U(1) Symmetry in the 3D<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:math>Model with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mi>q</mml:mi></mml:msub></mml:math>Anisotropy

Lou, Jie; Sandvik, Anders W.; Balents, Leon

doi:10.1103/physrevlett.99.207203

Cited by 78 publications

(139 citation statements)

References 16 publications

(22 reference statements)

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“…To obtain them, we fixed the critical exponents β and ν to be those for the 3D XY universality class (ν = 0.672 and β = 0.348) 37 , while finetuned the critical temperature T c such that all the data points for m fall into one scaling function f (x). With T c thus obtained, we further fine-tuned the crossover exponent for m 6 , ν 6 , such that all the data points for The former value of the crossover exponent ν 6 (1.45 ±0.05) is consistent with previous estimation in the Potts model 35,36 , while the latter value (1.85 ±0.05) is relatively larger. The discrepancy stems from the presence of a high symmetric point at (J, D, G) = (0, 0, −1) near the latter parameter point.…”

Section: Emergent U (1) Symmetry Around the Critical Pointsupporting

confidence: 61%

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Nature of the possible magnetic phases in a frustrated hyperkagome iridate

Shindou

2016

Phys. Rev. B

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Based on Kitaev-Heisenberg model with Dzyaloshinskii-Moriya (DM) interactions, we studied nature of possible magnetic phases in frustrated hyperkagome iridate, Na4Ir3O8 (Na-438). Using Monte-Carlo simulation, we showed that the phase diagram is mostly covered by two competing magnetic ordered phases; Z2 symmetry breaking (SB) phase and Z6 SB phase, latter of which is stabilized by the classical order by disorder. These two phases are intervened by a first order phase transition line with Z8-like symmetry. The critical nature at the Z6 SB ordering temperature is characterized by the 3D XY universality class, below which U(1) to Z6 crossover phenomena appears; the Z6 spin anisotropy becomes irrelevant in a length scale shorter than a crossover length Λ * while becomes relevant otherwise. A possible phenomenology of polycrystalline Na-438 is discussed based on this crossover phenomena.

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Section: Emergent U (1) Symmetry Around the Critical Pointsupporting

confidence: 61%

“…The crossover system size and temperature can be evaluated from the FNS analysis on the XY order parameter m and Z 6 order parameter m 6 . The scaling argument [34][35][36] suggests that these two follow single-parameter scalings;…”

Section: Emergent U (1) Symmetry Around the Critical Pointmentioning

confidence: 99%

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

Shindou

2016

Phys. Rev. B

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“…The O(n) symmetry is not at all obvious in the Hamiltonian, but it nevertheless emerges, and controls the critical properties of the continuous phase transition at T c . In the sense of universality, the three-state mixed Potts model is similar to the O(2) model with a Z 6 perturbation [25], which also displays an emergent O(2) symmetry at criticality. For q > 3, the mixed Potts model has a low-temperature ordered phase that spontaneously breaks the (q − 1)-dimensional face-cubic symmetry.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Emergent O(n) symmetry in a series of three-dimensional Potts models

2016

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We study the q-state Potts model on a simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the other two directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the three-dimensional O(n) model with n = q − 1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q = 4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T = 0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.

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“…However, the anisotropy is relevant for T < T c and lengths larger than Λ ∝ (ξ ⊥ ) α6 where α 6 > 1 is an exponent characterizing the scaling dimension of the anisotropy. [14,49,50] Therefore, in a finite-system simulation, the order-by-disorder selection mechanism only takes place for L Λ. Therefore we either have to go to low temperatures or large systems.…”

Section: Monte-carlo Algorithmmentioning

confidence: 99%

Spin freezing in the disordered pyrochlore magnet NaCaCo2F7 : NMR studies and Monte Carlo simulations

et al. 2017

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We present results of 23 Na and 19 F nuclear magnetic resonance (NMR) measurements on NaCaCo2F7, a frustrated pyrochlore magnet with a Curie-Weiss temperature, ΘCW ≈ −140 K, and intrinsic bond disorder. Below 3.6 K both the 23 Na and 19 F spectra broaden substantially in comparison to higher temperatures accompanied by a considerable reduction (80 %) of the NMR signal intensity: This proves a broad quasi-static field distribution. The 19 F spin-lattice relaxation rate 19 (1/T1) exhibits a peak at 2.9 K already starting to develop below 10 K. We attribute the spin freezing to the presence of bond disorder. This is corroborated by large-scale Monte-Carlo simulations of a classical bond-disordered XY model on the pyrochlore lattice. The low freezing temperature, together with the very short magnetic correlation length not captured by the simulations, suggesting that quantum effects play a decisive role in NaCaCo2F7.PACS numbers: 75.10. Nr, 75.40.Gb, The pyrochlore lattice is one of the canonical lattices exhibiting geometric frustration. Pyrochlore oxides with the general formula R 2 T 2 O 7 (R = rare earth ion, T = Ti, Sn, Mo, Ir etc.) are characterized by strong frustration of the rare-earth magnetic moments and have been found to display a variety of fascinating low-temperature phases, including classical and quantum spin-ice regimes, quantum order-by-disorder, and exotic spin liquids [1][2][3].NaCaCo 2 F 7 is a recently synthesized A 2 B 2 X 7 -type pyrochlore [4]. Here, the B site hosts high-spin Co 2+ in CoF 6 octahedra, whereas the A site contains a random distribution of Na and Ca ions, giving rise to exchange (bond) disorder for the magnetic degrees of freedom. Bond disorder can lift degeneracies and lead to new unconventional ground states, both long-range ordered [5,6] and glassy [7][8][9][10].The uniform susceptibility of NaCaCo 2 F 7 displays a Curie-Weiss law with a characteristic temperature Θ CW ≈ −140 K and a moment of 6.1 µ B per Co, the latter suggesting an orbital contribution in addition to the S = 3/2 state of Co 2+ . Despite the Θ CW ≈ −140 K, the material does not display a long-range-ordered magnetic state down to temperatures of 0.6 K [4]. Instead, ac and dc susceptibility data indicate a spin freezing at T f ≈ 2.4 K [4], yielding a frustration index of f = Θ CW /T f ≈ 56. The observed entropy loss at the freezing transition is low, suggesting that magnetic entropy remains present at least down to 0.6 K. Inelastic neutron scattering (INS) results [11] for NaCaCo 2 F 7 show diffuse elastic scattering below 2.4 K. The momentum-space structure of the spin correlations below 2.5 meV has been interpreted in terms of XY-like antiferromagnetic clusters, indicating a local easy-plane anisotropy at low energies, whereas a signal corresponding to collinear correlations was found above this energy. The XY character together with the short detected correlation length of 16Å [11] appears to be at odds with the theoretical suggestion [6] that bond disorder in an XY pyrochlore magnet induces long-range m...

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Emergence of U(1) Symmetry in the 3DXYModel withZqAnisotropy

Abstract: We study the three-dimensional XY model with a Zq anisotropic term. At temperatures T Show more

Cited by 78 publications

References 16 publications

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

Emergent O(n) symmetry in a series of three-dimensional Potts models

Spin freezing in the disordered pyrochlore magnet NaCaCo2F7 : NMR studies and Monte Carlo simulations

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