On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Mudrov, Andrey; Varnashev, K. B.

doi:10.1134/1.1417166

Cited by 10 publications

(13 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This method, proposed in [16] and extensively reviewed in [17], makes no assumptions on the underlying microscopic description and studies CFTs based only on global and conformal symmetry, unitarity, and consistency with the operator algebra (crossing symmetry). In agreement with the experimental (20,2). The allowed region lies below the curves for the corresponding parameter values.…”

Section: Introductionsupporting

confidence: 88%

“…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: 50%

“…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%

See 2 more Smart Citations

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Henriksson

Stergiou

2021

SciPost Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionsupporting

confidence: 88%

Section: Introductionsupporting

confidence: 50%

Section: Results From Previous Studies In the Expansionmentioning

confidence: 99%

See 1 more Smart Citation

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Henriksson

Stergiou

2021

SciPost Phys.

View full text Add to dashboard Cite

show abstract

“…Past discussions include [46,47,48]. The β-functions for such theories have been determined to four loops [49,50] for m = 2 and are physically relevant for m = 2, n = 2, 3. For m = n = 2 this case with O(2) 2 symmetry is identical with the O(2) × O(2) symmetric theory, taking…”

Section: N Fixed Pointsmentioning

confidence: 99%

“…The polynomial f (x), as defined in (5.14), now has roots, apart from x = 0, given by For m = 2, n = 2, 3 results to four loops are given in [50] (where κ = −2ω). The fixed point realised for x * = x + corresponds to decoupled O(m) theories, this is the stable fixed point for m > 4.…”

Section: N Fixed Pointsmentioning

confidence: 99%

Seeking fixed points in multiple coupling scalar theories in the ε expansion

Osborn

Stergiou

2018

J. High Energ. Phys.

173

View full text Add to dashboard Cite

Fixed points for scalar theories in 4 − ε, 6 − ε and 3 − ε dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general framework with two couplings. The original maximal symmetry, O(N ), is broken to various subgroups, both discrete and continuous. A similar discussion is applied to the six dimensional case. Perturbative applications of the a-theorem are used to help classify potential fixed points. At lowest order in the ε-expansion it is shown that at fixed points there is a lower bound for a which is saturated at bifurcation points. arXiv:1707.06165v7 [hep-th]

show abstract

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

Calabrese

Parruccini

2004

Nuclear Physics B

View full text Add to dashboard Cite

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 + .

show abstract

On critical behavior of phase transitions in certain antiferromagnets with complicated ordering

Cited by 10 publications

References 22 publications

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Perturbative and nonperturbative studies of CFTs with MN global symmetry

Seeking fixed points in multiple coupling scalar theories in the ε expansion

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

Contact Info

Product

Resources

About