Chiral Critical Exponents of the Triangular-Lattice Antiferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>CsMnBr</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>as Determined by Polarized Neutron Scattering

Plakhty, V.P.; Kulda, J.; Visser, D.; Moskvin, E. V.; Wosnitza, J.

doi:10.1103/physrevlett.85.3942

Cited by 59 publications

(49 citation statements)

References 35 publications

(53 reference statements)

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“…In a beautiful experiment, Plakhty et al [86] have measured the so-called chiral critical exponents β c and γ c [120] in CsMnBr 3 . They have found values compatible with those found numerically in STA [120].…”

Section: The Numerical Situationmentioning

confidence: 99%

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Nonperturbative renormalization-group approach to frustrated magnets

2004

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This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems. We argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach -the effective average action method -that we have used to investigate the physics of frustrated magnets. First, we recall the treatment of the unfrustrated -O(N ) -case with this method. This allows to introduce its technical aspects. Then, we show how this method unables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. Firstly, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in qualitative and (semi-) quantitative agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudo-fixed point and that relies on a slowing-down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allows to explain the occurence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.

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Section: The Numerical Situationmentioning

confidence: 99%

“…In this section, we give the threshold functions associated with the theta cut-off, see Eq. (86). One has, for a = 0: (C18)…”

Section: Threshold Functions From the Theta Cut-offmentioning

confidence: 99%

Nonperturbative renormalization-group approach to frustrated magnets

2004

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“…Further experimental evidence in favor of a chiral continuous transition has been recently reported in Ref. [2], showing the simultaneous occurrence of spin and chiral order in the XY stacked triangular antiferromagnet (STA) CsMnBr 3 .…”

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confidence: 99%

“…At present there is no agreement on the nature of the phase transition, and in particular on the existence of a new chiral universality class [1]. See, e.g., the recent works [2][3][4] and Refs. [5][6][7] for reviews.…”

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confidence: 99%

Chiral exponents in frustrated spin models with noncollinear order

2001

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We compute the chiral critical exponents for the chiral transition in frustrated two-and threecomponent spin systems with noncollinear order, such as stacked triangular antiferromagnets (STA). For this purpose, we calculate and analyze the six-loop field-theoretical expansion of the renormalization-group function associated with the chiral operator. The results are in satisfactory agreement with those obtained in the recent experiment on the XY STA CsMnBr3 reported by V. P. Plakhty et al., Phys. Rev. Lett. 85, 3942 (2000), providing further support for the continuous nature of the chiral transition.PACS Numbers: 05.10. Cc, 05.70.Fh, 75.10.Hk, 64.60.Fr, The critical behavior of frustrated spin systems with noncollinear order is still a controversial issue, fieldtheoretical (FT) methods, Monte Carlo (MC) simulations, and experiments providing contradictory results in many cases. At present there is no agreement on the nature of the phase transition, and in particular on the existence of a new chiral universality class [1]. See, e.g., the recent works [2][3][4] and Refs. [5][6][7] for reviews.In magnets noncollinear order is due to frustration that may arise either because of the special geometry of the lattice, or from the competition of different kinds of interactions. Typical examples of systems of the first type are two-and three-component antiferromagnets on stacked triangular lattices [8]. Their behavior at the chiral transition may be modeled by a short-ranged Hamiltonian for N -component spin variables S a , defined on a stacked triangular lattice aswhere J < 0, the first sum is over nearest-neighbor pairs within triangular layers, and the second one is over orthogonal interlayer nearest neighbors. Frustration due to the competition of interactions is realized in helimagnets.In these models frustration is partially released by mutual spin canting and the degeneracy of the ground state is limited to global O(N ) spin rotations and reflections. At criticality one expects a breakdown of the symmetry from O(N ) in the high-temperature phase to O(N − 2) in the low-temperature phase, implying a matrix-like order parameter. In particular, the ground state of the XY systems shows the 120 o structure of Fig. 1, and it is Z 2 chirally degenerate according to whether the noncollinear spin configuration is right-or left-handed. The chiral degrees of freedom are related to the local quantity [1]where the summation runs over the three bonds of the given triangle. The definition of C ab can be straightforwardly generalized to the case of N -component spins. In a recent Letter [3] the issue has been studied by a continuous renormalization-group (RG) approach (see also Refs. [16,17]). The results favor a first-order transition, since no evidence of stable fixed points is found. According to this first-order transition picture, the apparent continuous critical phenomena observed in experiments are interpreted as first-order transitions, weak enough to effectively appear as second-order ones. Note however that the practical i...

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“…47,49 Also, most of experiments seem to be in accordance with the continuous transition. 50 However, the former point of view is quite intriguing, since it implies that the phase transition of the 2D quantum version of these systems at T = 0 may be the (quantum) fluctuation-driven first order type. Although the quantum second order phase transition and the related quantum critical phenomena have been comprehensively explored so far, 38,39,40,51,52,53 long-wavelength properties which emerge near the quantum fluctuation-driven first order transition have not been clarified sufficiently.…”

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confidence: 99%

Low-energy properties of two-dimensional quantum triangular antiferromagnets: Nonperturbative renormalization group approach

Fujimoto

2006

Phys. Rev. B

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We explore low temperature properties of quantum triangular Heisenberg antiferromagnets in two dimension in the vicinity of the quantum phase transition at zero temperature. Using the effective field theory described by the O(3) × O(2) matrix Ginzburg-Landau-Wilson model and the non-perturbative renormalization group method, we clarify how quantum and thermal fluctuations affect long-wavelength behaviors in the parameter region where the systems exhibit a fluctuationdriven first order transition to a long-range ordered state. We show that at finite temperatures the crossover from a quantum φ 6 theory to a renormalized two-dimensional classical nonlinear sigma model region appears, and in this crossover region, massless fluctuation modes with linear dispersion a la spin waves govern low-energy physics. Our results are partly in good agreement with the recent experimental observations for the two-dimensional triangular Heisenberg spin system, NiGa2S4.

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Chiral Critical Exponents of the Triangular-Lattice AntiferromagnetCsMnBr3as Determined by Polarized Neutron Scattering

Cited by 59 publications

References 35 publications

Nonperturbative renormalization-group approach to frustrated magnets

Nonperturbative renormalization-group approach to frustrated magnets

Chiral exponents in frustrated spin models with noncollinear order

Low-energy properties of two-dimensional quantum triangular antiferromagnets: Nonperturbative renormalization group approach

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