Abstract
The leading irrelevant perturbation, which controls the deviation of critical square lattice Ising model with periodic boundary conditions from its continuous CFT analog is identified. An explicit expression for the coupling constant in terms of the anisotropy parameter is found. We calculate the next to leading ∼ 1/N 2 corrections to the spectrum on both lattice theory and the perturbed CFT sides for several classes of states, always getting exact agreement. We discuss also how the perturbing operators and the higher integrals of motion are related.
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J.G.E. Brezin and J.Zinn-Justin, Field theoretical approach to critical phenomena, in Phase transitions and critical phenomena. Volume 6, C. Domb and J.L. Lebowitz eds., Academic Press, New York U.S.A. (1972).
J. Cardy, Conformal invariance, in Phase transitions and critical phenomena. Volume 11, C. Domb and J. L. Lebowitz eds., Academic Press, New York U.S.A. (1987).
J.L. Cardy, Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 275 (1986) 200 [INSPIRE].
E. Ising, Contribution to the theory of ferromagnetism, Z. Phys. 31 (1925) 253 [INSPIRE].
L. Onsager, Crystal statistics. 1. A Two-dimensional model with an order disorder transition, Phys. Rev. 65 (1944) 117 [INSPIRE].
R. Baxter, Exactly solved models in statistical mechanics, Dover books on physics, Dover Publications, U.S.A. (2007).
D.L. O’Brien, P.A. Pearce and S.O. Warnaar, Finitized conformal spectrum of the Ising model on the cylinder and torus, Physica A 228 (1996) 63.
R.E. Behrend, P.A. Pearce and D.L. O’Brien, Interaction-round-a-face models with fixed boundary conditions: The ABF fusion hierarchy, J. Statist. Phys. 84 (1996) 1 [hep-th/9507118] [INSPIRE].
R.E. Behrend, P.A. Pearce, V.B. Petkova and J.-B. Zuber, Boundary conditions in rational conformal field theories, Nucl. Phys. B 570 (2000) 525 [hep-th/9908036] [INSPIRE].
C. Chui, C. Mercat, W. P. Orrick and P.A. Pearce, Integrable lattice realizations of conformal twisted boundary conditions, Phys. Lett. B 517 (2001) 429.
C.H.O. Chui, C. Mercat and P.A. Pearce, Integrable and conformal twisted boundary conditions for sl(2) A-D-E lattice models, J. Phys. A 36 (2003) 2623 [hep-th/0210301] [INSPIRE].
H.W.J. Bloete, J.L. Cardy and M.P. Nightingale, Conformal invariance, the central charge and universal finite size amplitudes at criticality, Phys. Rev. Lett. 56 (1986) 742 [INSPIRE].
I. Affleck, Universal term in the free energy at a critical point and the conformal anomaly, Phys. Rev. Lett. 56 (1986) 746 [INSPIRE].
J. Salas and A.D. Sokal, Universal amplitude ratios in the critical two-dimensional Ising model on a torus, J. Statist. Phys. 98 (2000) 551 [cond-mat/9904038] [INSPIRE].
P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Graduate Texts in Contemporary Physics, Springer, Germany (1997).
J.L. Cardy, Operator content of two-dimensional conformally invariant theories, Nucl. Phys. B 270 (1986) 186 [INSPIRE].
A.B. Zamolodchikov, Renormalization group and perturbation theory near fixed points in two-dimensional field theory, Sov. J. Nucl. Phys. 46 (1987) 1090 [INSPIRE].
R. Sasaki and I. Yamanaka, Virasoro algebra, vertex operators, quantum sine-Gordon and solvable quantum field theories, Adv. Stud. Pure Math. 16 (1988) 271.
T. Eguchi and S.-K. Yang, Deformations of conformal field theories and soliton equations, Phys. Lett. B 224 (1989) 373 [INSPIRE].
V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz, Commun. Math. Phys. 177 (1996) 381 [hep-th/9412229] [INSPIRE].
A. Morin-Duchesne, J. Rasmussen and P. Ruelle, Integrability and conformal data of the dimer model, J. Phys. A 49 (2016) 174002 [arXiv:1507.04193] [INSPIRE].
P. Reinicke, Analytical and nonanalytical corrections to finite size scaling, J. Phys. A 20 (1987) 5325 [INSPIRE].
A. Poghosyan, R. Kenna and N. Izmailian, The critical ising model on a torus with a defect line, Europhys. Lett. 111 (2015) 60010.
A. Poghosyan, N. Izmailian and R. Kenna, Exact solution of the critical Ising model with special toroidal boundary conditions, Phys. Rev. E 96 (2017) 062127 [arXiv:1610. 07855] [INSPIRE].
N.S. Izmailian and C.-K. Hu, Exact universal amplitude ratios for two-dimensional ising models and a quantum spin chain, Phys. Rev. Lett. 86 (2001) 5160.
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ArXiv ePrint: 1908.06291
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Poghosyan, A. Shaping lattice through irrelevant perturbation: Ising model. J. High Energ. Phys. 2019, 83 (2019). https://doi.org/10.1007/JHEP11(2019)083
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DOI: https://doi.org/10.1007/JHEP11(2019)083