Abstract
We make precise determinations of the leading scaling dimensions and operator product expansion (OPE) coefficients in the 3d Ising, O(2), and O(3) models from the conformal bootstrap with mixed correlators. We improve on previous studies by scanning over possible relative values of the leading OPE coefficients, which incorporates the physical information that there is only a single operator at a given scaling dimension. The scaling dimensions and OPE coefficients obtained for the 3d Ising model, (Δ σ , Δ ϵ , λ σσϵ , λ ϵϵϵ ) = (0.5181489(10), 1.412625(10), 1.0518537(41), 1.532435(19) , give the most precise determinations of these quantities to date.
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References
S. Ferrara, A.F. Grillo and R. Gatto, Tensor representations of conformal algebra and conformally covariant operator product expansion, Annals Phys. 76 (1973) 161 [INSPIRE].
A.M. Polyakov, Nonhamiltonian approach to conformal quantum field theory, Zh. Eksp. Teor. Fiz. 66 (1974) 23 [INSPIRE].
S. El-Showk et al., Solving the 3D Ising model with the conformal bootstrap, Phys. Rev. D 86 (2012) 025022 [arXiv:1203.6064] [INSPIRE].
S. El-Showk et al., Solving the 3d Ising model with the conformal bootstrap II. c-Minimization and precise critical exponents, J. Stat. Phys. 157 (2014) 869 [arXiv:1403.4545] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping mixed correlators in the 3D Ising model, JHEP 11 (2014) 109 [arXiv:1406.4858] [INSPIRE].
D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [INSPIRE].
F. Gliozzi, More constraining conformal bootstrap, Phys. Rev. Lett. 111 (2013) 161602 [arXiv:1307.3111] [INSPIRE].
F. Gliozzi and A. Rago, Critical exponents of the 3d Ising and related models from conformal bootstrap, JHEP 10 (2014) 042 [arXiv:1403.6003] [INSPIRE].
F. Kos, D. Poland, D. Simmons-Duffin and A. Vichi, Bootstrapping the O(N ) archipelago, JHEP 11 (2015) 106 [arXiv:1504.07997] [INSPIRE].
F. Kos, D. Poland and D. Simmons-Duffin, Bootstrapping the O(N ) vector models, JHEP 06 (2014) 091 [arXiv:1307.6856] [INSPIRE].
Y. Nakayama and T. Ohtsuki, Five dimensional O(N )-symmetric CFTs from conformal bootstrap, Phys. Lett. B 734 (2014) 193 [arXiv:1404.5201] [INSPIRE].
M. Lemos and P. Liendo, Bootstrapping \( \mathcal{N} \) = 2 chiral correlators, JHEP 01 (2016) 025 [arXiv:1510.03866] [INSPIRE].
C. Behan, PyCFTBoot: a flexible interface for the conformal bootstrap, arXiv:1602.02810 [INSPIRE].
Y. Nakayama and T. Ohtsuki, Conformal bootstrap dashing hopes of emergent symmetry, arXiv:1602.07295 [INSPIRE].
J.A. Lipa, J.A. Nissen, D.A. Stricker, D.R. Swanson and T.C.P. Chui, Specific heat of liquid helium in zero gravity very near the lambda point, Phys. Rev. B 68 (2003) 174518 [INSPIRE].
M. Campostrini, M. Hasenbusch, A. Pelissetto and E. Vicari, The critical exponents of the superfluid transition in 4 He, Phys. Rev. B 74 (2006) 144506 [cond-mat/0605083] [INSPIRE].
M. Hasenbusch, Finite size scaling study of lattice models in the three-dimensional Ising universality class, Phys. Rev. B 82 (2010) 174433 [arXiv:1004.4486] [INSPIRE].
S. Rychkov, unpublished.
M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi and E. Vicari, Critical exponents and equation of state of the three-dimensional Heisenberg universality class, Phys. Rev. B 65 (2002) 144520 [cond-mat/0110336] [INSPIRE].
M. Hasenbusch and E. Vicari, Anisotropic perturbations in three-dimensional O(N )-symmetric vector models, Phys. Rev. B 84 (2011) 125136 [arXiv:1108.0491].
M. Caselle, G. Costagliola and N. Magnoli, Numerical determination of the operator-product-expansion coefficients in the 3D Ising model from off-critical correlators, Phys. Rev. D 91 (2015) 061901 [arXiv:1501.04065] [INSPIRE].
G. Costagliola, Operator product expansion coefficients of the 3D Ising model with a trapping potential, Phys. Rev. D 93 (2016) 066008 [arXiv:1511.02921] [INSPIRE].
Z. Komargodski and D. Simmons-Duffin, The random-bond Ising model in 2.01 and 3 dimensions, arXiv:1603.04444 [INSPIRE].
M. Caselle, G. Costagliola and N. Magnoli, Conformal perturbation of off-critical correlators in the 3D Ising universality class, Phys. Rev. D 94 (2016) 026005 [arXiv:1605.05133] [INSPIRE].
C. Beem, L. Rastelli and B.C. van Rees, The \( \mathcal{N} \) = 4 superconformal bootstrap, Phys. Rev. Lett. 111 (2013) 071601 [arXiv:1304.1803] [INSPIRE].
C. Beem, M. Lemos, L. Rastelli and B.C. van Rees, The (2, 0) superconformal bootstrap, Phys. Rev. D 93 (2016) 025016 [arXiv:1507.05637] [INSPIRE].
H. Iha, H. Makino and H. Suzuki, Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach, Prog. Theor. Exp. Phys. 2016 (2016) 053B03 [arXiv:1603.01995] [INSPIRE].
D. Poland, D. Simmons-Duffin and A. Vichi, Carving out the space of 4D CFTs, JHEP 05 (2012) 110 [arXiv:1109.5176] [INSPIRE].
D. Poland and A. Stergiou, Exploring the minimal 4D \( \mathcal{N} \) = 1 SCFT, JHEP 12 (2015) 121 [arXiv:1509.06368] [INSPIRE].
L. Iliesiu et al., Bootstrapping 3D fermions, JHEP 03 (2016) 120 [arXiv:1508.00012] [INSPIRE].
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ArXiv ePrint: 1603.04436
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Kos, F., Poland, D., Simmons-Duffin, D. et al. Precision islands in the Ising and O(N ) models. J. High Energ. Phys. 2016, 36 (2016). https://doi.org/10.1007/JHEP08(2016)036
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DOI: https://doi.org/10.1007/JHEP08(2016)036