Built on

L. Pauling, “The application of the quantum mechanics to the structure of the hydrogen molecule and hydrogen molecule-ion and to related problems,” Chem. Rev
1928
Earlier work this paper cites.
P. A. Dirac, “Wave equations in conformal space,” Annals Math
1936
Earlier work this paper cites.
H. Osborn, “Conformal blocks for arbitrary spin in two dimensions,” Phys. Lett
Original
1941
Earlier work this paper cites.
L. Onsager, “Crystal statistics I: A two-dimension model with an order-disorder transition,” Phys. Rev
1944
Earlier work this paper cites.
F. J. Dyson, “Existence of a phase-transition in a one-dimensional Ising ferromagnet,” Commun. Math. Phys
1969
Earlier work this paper cites.
M. E. Fisher, S.-K. Ma and B. G. Nickel, “Critical exponents for long-range interactions,” Phys. Rev. Lett
1972
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
J. Sak, “Recursion relations and fixed points for ferromagnets with long-range interactions,” Phys. Rev
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Theor. Fiz
1974
Earlier work this paper cites.
A. B. Zamolodchikov, “Renormalization group and perturbation theory near fixed points in two-dimensional field theory,” Sov. J. Nucl. Phys
1987
Earlier work this paper cites.
K. De’Bell, A. B. MacIsaac and J. P. Whitehead, “Dipolar effects in magnetic thin films and quasi-two-dimensional systems,” Rev. Mod. Phys
2000
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys
2001
Earlier work this paper cites.
D. Dantchev and J. Rudnick, “Subleading long-range interactions and violations of finite size scaling,” Eur. Phys. J. B
2001
Earlier work this paper cites.
S. T. Bramwell, M. J. Harris, B. C. den Hertog, M. J. P. Gingras, J. S. Gardner, D. F. McMorrow, A. R. Wildes, A. L. Cornelius, J. D. M. Champion, R. G. Meiko and T. Fennell, “Spin correlations in Ho 2 Ti 2 O 7 \mathrm{Ho}_{2}\mathrm{Ti}_{2}\mathrm{O}_{7} : A dipolar spin ice system,” Phys. Rev. Lett
2001
Earlier work this paper cites.
E. Luijten and H. W. J. Blöte, “The boundary between long-range and short-range critical behavior,” Phys. Rev. Lett
2002
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Superconformal symmetry, correlation functions and the operator product expansion,” Nucl. Phys
2002
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys
2004
Earlier work this paper cites.
PhD thesis, Cergy-Pontoise University, 2005
S. Reynal, Phase transitions in long-range spin models: The power of generalized ensembles · 2005
Earlier work this paper cites.
R. Rattazzi, S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
D. Larson, H. G. Katzgraber, M. A. Moore and A. P. Young, “Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions,” Phys. Rev
Original
2010
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning conformal correlators,” JHEP
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning conformal blocks,” JHEP
Original
2011
Earlier work this paper cites.
S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, “Solving the 3D Ising model with the conformal bootstrap,” Phys. Rev
Original
2012
Earlier work this paper cites.
J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk and J. J. Bollinger, “Engineered, two-dimensional Ising interations in a trapped-ion quantum simulator with hundreds of spins,” Nature
2012
Earlier work this paper cites.
R. A. Baños, L. A. Fernandez, V. Martin-Mayor and A. P. Young, “The correspondence between long-range and short-range spin glasses,” Phys. Rev
Original
2012
Earlier work this paper cites.

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2018

Bootstrapping the long-range Ising model in three dimensions

Behan, Connor

Understand

The 3D Ising model and the generalized free scalar of dimension at least 0.75 belong to a continuous line of nonlocal fixed points, each referred to as a long-range Ising model.

They can be distinguished by the dimension of the lightest spin-2 operator, which interpolates between 3 and 3.5 if we focus on the non-trivial part of the fixed line.
A property common to all such theories is the presence of three relevant conformal primaries, two of which form a shadow pair.
This pair is analogous to a superconformal multiplet in that it enforces relations between certain conformal blocks.

Built on

L. Pauling, “The application of the quantum mechanics to the structure of the hydrogen molecule and hydrogen molecule-ion and to related problems,” Chem. Rev
1928
Earlier work this paper cites.
P. A. Dirac, “Wave equations in conformal space,” Annals Math
1936
Earlier work this paper cites.
H. Osborn, “Conformal blocks for arbitrary spin in two dimensions,” Phys. Lett
Original
1941
Earlier work this paper cites.
L. Onsager, “Crystal statistics I: A two-dimension model with an order-disorder transition,” Phys. Rev
1944
Earlier work this paper cites.
F. J. Dyson, “Existence of a phase-transition in a one-dimensional Ising ferromagnet,” Commun. Math. Phys
1969
Earlier work this paper cites.
M. E. Fisher, S.-K. Ma and B. G. Nickel, “Critical exponents for long-range interactions,” Phys. Rev. Lett
1972
Earlier work this paper cites.
S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys
1973
Earlier work this paper cites.
J. Sak, “Recursion relations and fixed points for ferromagnets with long-range interactions,” Phys. Rev
1973
Earlier work this paper cites.
A. M. Polyakov, “Nonhamiltonian approach to conformal quantum field theory,” Zh. Eksp. Theor. Fiz
1974
Earlier work this paper cites.
A. B. Zamolodchikov, “Renormalization group and perturbation theory near fixed points in two-dimensional field theory,” Sov. J. Nucl. Phys
1987
Earlier work this paper cites.
K. De’Bell, A. B. MacIsaac and J. P. Whitehead, “Dipolar effects in magnetic thin films and quasi-two-dimensional systems,” Rev. Mod. Phys
2000
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal four point functions and the operator product expansion,” Nucl. Phys
2001
Earlier work this paper cites.
D. Dantchev and J. Rudnick, “Subleading long-range interactions and violations of finite size scaling,” Eur. Phys. J. B
2001
Earlier work this paper cites.
S. T. Bramwell, M. J. Harris, B. C. den Hertog, M. J. P. Gingras, J. S. Gardner, D. F. McMorrow, A. R. Wildes, A. L. Cornelius, J. D. M. Champion, R. G. Meiko and T. Fennell, “Spin correlations in Ho 2 Ti 2 O 7 \mathrm{Ho}_{2}\mathrm{Ti}_{2}\mathrm{O}_{7} : A dipolar spin ice system,” Phys. Rev. Lett
2001
Earlier work this paper cites.
E. Luijten and H. W. J. Blöte, “The boundary between long-range and short-range critical behavior,” Phys. Rev. Lett
2002
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Superconformal symmetry, correlation functions and the operator product expansion,” Nucl. Phys
2002
Earlier work this paper cites.
F. A. Dolan and H. Osborn, “Conformal partial waves and the operator product expansion,” Nucl. Phys
2004
Earlier work this paper cites.
PhD thesis, Cergy-Pontoise University, 2005
S. Reynal, Phase transitions in long-range spin models: The power of generalized ensembles · 2005
Earlier work this paper cites.
R. Rattazzi, S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4D CFT,” JHEP
Original
2008
Earlier work this paper cites.
D. Larson, H. G. Katzgraber, M. A. Moore and A. P. Young, “Numerical studies of a one-dimensional 3-spin spin-glass model with long-range interactions,” Phys. Rev
Original
2010
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning conformal correlators,” JHEP
Original
2011
Earlier work this paper cites.
M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning conformal blocks,” JHEP
Original
2011
Earlier work this paper cites.
S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, “Solving the 3D Ising model with the conformal bootstrap,” Phys. Rev
Original
2012
Earlier work this paper cites.
J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk and J. J. Bollinger, “Engineered, two-dimensional Ising interations in a trapped-ion quantum simulator with hundreds of spins,” Nature
2012
Earlier work this paper cites.
R. A. Baños, L. A. Fernandez, V. Martin-Mayor and A. P. Young, “The correspondence between long-range and short-range spin glasses,” Phys. Rev
Original
2012
Earlier work this paper cites.