Critical behavior of certain antiferromagnets with complicated ordering: Four-loop<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ɛ</mml:mi></mml:math>-expansion analysis

Mudrov, Andrey; Varnashev, K. B.

doi:10.1103/physrevb.64.214423

Cited by 13 publications

(22 citation statements)

References 43 publications

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“…First, we focus on the first kink, which approaches the value (∆ φ , ∆ X ) = (0.5, 2) as m → ∞. In [15], it was observed that this limit is compatible with the results in the expansion [3,21,24,25] expanded at large m, where indeed ∆ φ → d−2 2 and ∆ X → 2 up to m −1 corrections. We show here that the m −1 corrections can be computed in a perturbative expansion similar to the usual large N expansion of the O(N ) model (see e.g.…”

Section: Introductionsupporting

confidence: 56%

“…While the critical exponents corresponding to the second kink show reasonable agreement, within uncertainties, with the results of [8,19], neither set of values is compatible with the predictions from the expansion, which gives β = 0.370 (5) and ν = 0.715(10) [20,21]. 3 Although it was speculated in [15] that the first kink may be related to the expansion through the large m limit, the results of that study were not sufficient to make any conclusive statements.…”

Section: Introductionsupporting

confidence: 49%

“…Conformal field theories with MN symmetry have been studied in the d = 4 − expansion over a long time, [20,21,24,25,39,40], most recently in section 5.2.2. of [3]. From the beta functions of the couplings λ and g in the Lagrangian (1), four fixed points are found in the expansion: mn free fields, n decoupled critical O(m) models, the critical O(mn) model, and the perturbative MN CFT.…”

Section: Results From Previous Studies In the Expansionmentioning

confidence: 99%

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Perturbative and nonperturbative studies of CFTs with MN global symmetry

Henriksson

Stergiou

2021

SciPost Phys.

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Fixed points in three dimensions described by conformal field theories with \ensuremath{M N}_{m,n} = O(m)^n\rtimes S_nMNm,n=O(m)n⋊Sn global symmetry have extensive applications in critical phenomena. Associated experimental data for m=n=2m=n=2 suggest the existence of two non-trivial fixed points, while the \varepsilonε expansion predicts only one, resulting in a puzzling state of affairs. A recent numerical conformal bootstrap study has found two kinks for small values of the parameters mm and nn, with critical exponents in good agreement with experimental determinations in the m=n=2m=n=2 case. In this paper we investigate the fate of the corresponding fixed points as we vary the parameters mm and nn. We find that one family of kinks approaches a perturbative limit as mm increases, and using large spin perturbation theory we construct a large mm expansion that fits well with the numerical data. This new expansion, akin to the large NN expansion of critical O(N)O(N) models, is compatible with the fixed point found in the \varepsilonε expansion. For the other family of kinks, we find that it persists only for n=2n=2, where for large mm it approaches a non-perturbative limit with \Delta_\phi\approx 0.75Δϕ≈0.75. We investigate the spectrum in the case \ensuremath{M N}_{100,2}MN100,2 and find consistency with expectations from the lightcone bootstrap.

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Section: Introductionsupporting

confidence: 56%

Section: Introductionsupporting

confidence: 49%

Section: Results From Previous Studies In the Expansionmentioning

confidence: 99%

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Perturbative and nonperturbative studies of CFTs with MN global symmetry

Henriksson

Stergiou

2021

SciPost Phys.

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“…14 does not correspond to the O 2,2 chiral fixed point. In [39] it was suggested that this kink may correspond to the fully-interacting theory of the expansion analyzed in [71][72][73][74]. To continue our search for the O 2,2 chiral fixed point, we obtain a bound on the dimension of the first scalar operator in the WX representation.…”

Section: Single Correlator In the O(2) × O(2) Casementioning

confidence: 96%

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

2020

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Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with O(m)\times O(n)O(m)×O(n) global symmetry in d=3d=3 spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in \varepsilon=4-dε=4−d and in 1/n1/n, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for O(2)\times O(n)O(2)×O(n) theories for various values of nn. Some of these islands can be attributed to fixed points predicted by perturbative methods like the \varepsilonε and large-nn expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions.

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“…[16], with the four-loop ǫ expansion of the so called tetragonal model Ref. [39]. The value of n H (m, 4 − ǫ) coincides with N c /m, where N c is the marginal spin dimensionality of the cubic model obtained in [40], according to the symmetry argument of Refs.…”

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confidence: 99%

Five-loop ϵ expansion for O(n)×O(m) spin models

Calabrese

Parruccini

2004

Nuclear Physics B

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We compute the Renormalization Group functions of a Landau-GinzburgWilson Hamiltonian with O(n)×O(m) symmetry up to five-loop in Minimal Subtraction scheme. The line n + (m, d), which limits the region of secondorder phase transition, is reconstructed in the framework of the ǫ = 4 − d expansion for generic values of m up to O(ǫ 5 ). For the physically interesting case of noncollinear but planar orderings (m = 2) we obtain n + (2, 3) = 6.1(6) by exploiting different resummation procedures. We substantiate this results re-analyzing six-loop fixed dimension series with pseudo-ǫ expansion, obtaining n + (2, 3) = 6.22(12). We also provide predictions for the critical exponents characterizing the second-order phase transition occurring for n > n + .

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Critical behavior of certain antiferromagnets with complicated ordering: Four-loopɛ-expansion analysis

Cited by 13 publications

References 43 publications

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D

Five-loop ϵ expansion for O(n)×O(m) spin models

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