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Gracey, J.A.

doi:10.1103/physreve.66.027102

Cited by 20 publications

(13 citation statements)

References 26 publications

(44 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…∆ φ is known to order 1/N 3 while ∆ S has only been computed to order 1/N 2 (see [21] and references therein). The crossover exponent connected to ∆ T was also computed to order 1/N 2 in [54]. The results are:…”

Section: Results and Comparison To O(n ) Vector Modelsmentioning

confidence: 99%

Bootstrapping the O(N ) vector models

Kos

Poland

Simmons-Duffin

2014

J. High Energ. Phys.

320

602

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We study the conformal bootstrap for 3D CFTs with O(N ) global symmetry. We obtain rigorous upper bounds on the scaling dimensions of the first O(N ) singlet and symmetric tensor operators appearing in the φ i × φ j OPE, where φ i is a fundamental of O(N ). Comparing these bounds to previous determinations of critical exponents in the O(N ) vector models, we find strong numerical evidence that the O(N ) vector models saturate the bootstrap constraints at all values of N . We also compute general lower bounds on the central charge, giving numerical predictions for the values realized in the O(N ) vector models. We compare our predictions to previous computations in the 1/N expansion, finding precise agreement at large values of N .

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Section: Results and Comparison To O(n ) Vector Modelsmentioning

confidence: 99%

Bootstrapping the O(N ) vector models

Kos

Poland

Simmons-Duffin

2014

J. High Energ. Phys.

320

602

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show abstract

“…The large-n expansion of the crossover exponent φ c as [35] given in Eqs. ( 38) and ( 53) was calculated in [46] up to 1/n 2 .…”

Section: Connection To the Large-n Expansionmentioning

confidence: 99%

Fractal dimension of critical curves in the O(n) -symmetric ϕ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising,
Kompaniets
¹
,
Wiese
²

2020
Phys. Rev. E
44
8
49
0
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We calculate the fractal dimension d f of critical curves in the O(n) symmetric ( φ 2 ) 2 -theory in d = 4 − ε dimensions at 6-loop order. This gives the fractal dimension of loop-erased random walks at n = −2, selfavoiding walks (n = 0), Ising lines (n = 1), and XY lines (n = 2), in agreement with numerical simulations. It can be compared to the fractal dimension d tot f of all lines, i.e. backbone plus the surrounding loops, identical to= νd f is the crossover exponent, describing a system with mass anisotropy. Introducing a novel self-consistent resummation procedure, and combining it with analytic results in d = 2 allows us to give improved estimates in d = 3 for all relevant exponents at 6-loop order.

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“…On the other hand, theories without a symmetry forbidding this exchange are expected to exchange t itself as the first traceless symmetric operator. In that case we can assume the exchange of t itself and bound the next traceless symmetric operator ), according to large N estimates [59]. The green region shows the prediction for the ARP 3 model from lattice computations.…”

Section: Bounds On Operator Dimensions and Ope Coefficientsmentioning

confidence: 99%

Bootstrapping traceless symmetric $O(N)$ scalars

Reehorst¹,

Refinetti²,

Vichi³

2020

Preprint

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We use numerical bootstrap techniques to study correlation functions of a traceless symmetric tensors of O(N ) with two indexes t ij . We obtain upper bounds on operator dimensions for all the relevant representations and several values of N . We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case N = 4, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model ARP 3 . Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving t and the lowest dimension scalar singlet.

show abstract

Crossover exponent inO(N)φ4theory at

Cited by 20 publications

References 26 publications

Bootstrapping the O(N ) vector models

Bootstrapping the O(N ) vector models

Fractal dimension of critical curves in the O(n) -symmetric ϕ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising,
Kompaniets
¹
,
Wiese
²

2020
Phys. Rev. E
44
8
49
0
View full text Add to dashboard Cite

Bootstrapping traceless symmetric $O(N)$ scalars

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Product

Resources

About

Crossover exponent inO(N)φ4theory at

Cited by 20 publications

References 26 publications

Bootstrapping the O(N ) vector models

Bootstrapping the O(N ) vector models

Fractal dimension of critical curves in the O(n) -symmetric ϕ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising, Kompaniets1, Wiese2 2020Phys. Rev. E448490View full textAdd to dashboardCite

Bootstrapping traceless symmetric $O(N)$ scalars

Contact Info

Product

Resources

About

Fractal dimension of critical curves in the O(n) -symmetric ϕ4 model and crossover exponent at 6-loop order: Loop-erased random walks, self-avoiding walks, Ising,
Kompaniets
¹
,
Wiese
²

2020
Phys. Rev. E
44
8
49
0
View full text Add to dashboard Cite