On the criticality of frustrated spin systems with noncollinear order

Holovatch, Yu.; Ivaneyko, Dmytro; Delamotte, Bertrand

doi:10.1088/0305-4470/37/11/002

Cited by 33 publications

(14 citation statements)

References 26 publications

(59 reference statements)

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“…This result is interpreted as the occurrence of a second-order transition for values of N above N c ͑d͒ and a first-order transition for values of N below N c ͑d͒. In the ⑀ expansion [35][36][37] and within the NPRG, 1,38-41 the lines N c ͑d͒ are both monotonic and are very similar ͑see Fig. 7͒.…”

Section: A Frustrated Models In D =3mentioning

confidence: 77%

“…31,33,34 This fact has led to the hypothesis of a Kosterlitz-Thouless-type behavior induced by Z 2 topological defects for Heisenberg spins. 33 The second explanation is based on both the ⑀ =4−d ͑or pseudo-⑀͒ expansion [35][36][37] and the nonperturbative RG ͑NPRG͒ approaches. 1,[38][39][40][41] In these approaches, one finds that there exists, within the ͑d , N͒ plane, a line N c ͑d͒ that separates a second-order region for N Ͼ N c from a first-order region for N Ͻ N c .…”

Section: Introductionmentioning

confidence: 99%

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Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

et al. 2010

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We show that the critical behavior of two-and three-dimensional frustrated magnets cannot reliably be described from the known five-and six-loop perturbative renormalization-group results. Our conclusions are based on a careful reanalysis of the resummed perturbative series obtained within the zero-momentum massive scheme. In three dimensions, the critical exponents for XY and Heisenberg spins display strong dependences on the parameters of the resummation procedure and on the loop order. This behavior strongly suggests that the fixed points found are in fact spurious. In two dimensions, we find, as in the O͑N͒ case, that there is apparent convergence of the critical exponents but toward erroneous values. As a consequence, the interesting question of the description of the crossover/transition induced by Z 2 topological defects in two-dimensional frustrated Heisenberg spins remains open.

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Section: A Frustrated Models In D =3mentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

et al. 2010

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“…However, it usually appears only in a tiny region of the global phase diagram. For classical AF Heisenberg and XY models on stacked triangular lattices, Monte-Carlo simulations and field-theoretical analyses have suggested a single phase transition from paramagnet to helical magnet, which is either weakly first-order or a second-order one, which belongs to a different universality class from the O(N) model [27,28,29]. Then, the chiral spin liquid-crystal phase does not appear.…”

mentioning

confidence: 99%

Chiral Spin Pairing in Helical Magnets

Onoda

Nagaosa

2007

Phys. Rev. Lett.

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A concept of chiral spin pairing is introduced to describe a vector-chiral liquid-crystal order in frustrated spin systems. It is found that the chiral spin pairing is induced by the coupling to phonons through the Dzyaloshinskii-Moriya interaction and the four-spin exchange interaction of the Coulomb origin under the edge-sharing network of magnetic and ligand ions. This produces two successive second-order phase transitions upon cooling: an O(2) chiral spin nematic, i.e., spin cholesteric, order appears with an either parity, and then the O(2) symmetry is broken to yield a helical magnetic order. Possible candidate materials are also discussed as new multiferroic systems.PACS numbers: 75.10. Hk, 05.50.+q, 63.70.+h, The chirality in the electronic spin texture introduced by a geometrical frustration and/or the relativistic spinorbit interaction has been one of the key concepts in strongly correlated electron systems. The scalar spin chirality [1, 2, 3], i.e., the scalar triple product of three noncoplanar spins, is odd under the time-reversal (T ) and even under the space-inversion (I), and gives rise to a large anomalous Hall effect [4,5,6,7,8]. On the other hand, central to this Letter is the vector spin chirality [9], i.e., the vector product of two noncollinear spins. It is T -even and I-odd, and can produce the ferroelectric polarization in Mott insulators through the spin-orbit interaction [10,11,12,13,14,15,16,17], even for spin-1/2 systems [17,18,19].The vector-chiral spin order is realized in conventional helical magnets. In principle, it is even possible that the chiral or parity symmetry is broken but the time-reversal symmetry is not. This state having finite spin correlation lengths is categorized into a liquid or a liquid crystal of spins, which is of our main interest, while the magnetically ordered state into a solid. The issue of the chiral spin order in the absence of any magnetic order is not only a problem of statistical mechanics, but has been intensively studied since the discovery of high-T c cuprates, and even gives a new "multiferroic" phenomenon which has attracted current great interests, as discussed below. However, conditions for the order being stabilized have not been fully understood.It has been argued that the vector or pseudoscalar chiral ordering [20,21,22] takes place separately from the XY transition in the antiferromagnetic (AF) XY model on the triangular lattice [23]. The intermediate phase is characterized by the vector-chiral order. It has also been obtained for frustrated quantum spin systems in one dimension [24], and discussed in two dimensions [25] and for odd-time states [26]. However, it usually appears only in a tiny region of the global phase diagram. For classical AF Heisenberg and XY models on stacked triangular lattices, Monte-Carlo simulations and field-theoretical analyses have suggested a single phase transition from paramagnet to helical magnet, which is either weakly first-order or a second-order one, which belongs to a different universality class from t...

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“…Since the superfluid transition is likely to first order, as shown in this paper, the possible existence of a ferromagnetic transition without BEC remains an open question. Figure 8 shows the schematic flow diagram of the threedimensional O(N )×O(2) model according to perturbative RG near four dimensions [7][8][9][10][11][12] and NPRG [13][14][15][16]. Above a critical value N c , the transition is second order and governed by a (stable) "chiral" fixed point (denoted by C + in Fig.…”

Section: Ferromagnetic Transition Without Superfluiditymentioning

confidence: 99%

First-order phase transitions in spinor Bose gases and frustrated magnets

Debelhoir¹,

Dupuis²

2016

Phys. Rev. A

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We show that phase transitions in spin-one Bose gases and stacked triangular Heisenberg antiferromagnets -an example of frustrated magnets with competing interactions -are described by the same Landau-Ginzburg-Wilson Hamiltonian with O(3)×O(2) symmetry. In agreement with previous nonperturbative-renormalization-group studies of the three-dimensional O(3)×O(2) model, we find that the transition from the normal phase to the superfluid ferromagnetic phase in a spin-one Bose gas is weakly first order and shows pseudoscaling behavior. The (nonuniversal) pseudoscaling exponent ν is fully determined by the scattering lengths a0 and a2. We provide estimates of ν in 87 Rb, 41 K and 7 Li atom gases which can be tested experimentally. We argue that pseudoscaling comes from either a crossover phenomena due to proximity of the O(6) Wilson-Fisher fixed point ( 87 Rb and 41 K) or the existence of two unphysical fixed points (with complex coordinates) which slow down the RG flow ( 7 Li). These unphysical fixed points are a remnant of the chiral and antichiral fixed points that exist in the O(N )×O(2) model when N is larger than Nc 5.3 (the transition being then second order and controlled by the chiral fixed point). Finally, we discuss a O(2)×O(2) lattice model and show that our results, even though we find the transition to be first order, are compatible with Monte Carlo simulations yielding an apparent second-order transition.

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On the criticality of frustrated spin systems with noncollinear order

Cited by 33 publications

References 26 publications

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

Relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions

Chiral Spin Pairing in Helical Magnets

First-order phase transitions in spinor Bose gases and frustrated magnets

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