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Benchmarking the Ising Universality Class in $3 \le d < 4$ dimensions (2210.03051v3)

Published 6 Oct 2022 in hep-th and cond-mat.stat-mech

Abstract: The Ising critical exponents $\eta$, $\nu$ and $\omega$ are determined up to one-per-thousand relative error in the whole range of dimensions $3 \le d < 4$, using numerical conformal-bootstrap techniques. A detailed comparison is made with results by the resummed epsilon-expansion in varying dimension, the analytic bootstrap, Monte Carlo and non-perturbative renormalization-group methods, finding very good overall agreement. Precise conformal field theory data of scaling dimensions and structure constants are obtained as functions of dimension, improving on earlier findings, and providing benchmarks in $3 \le d < 4$.

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References (60)
  1. K. G. Wilson and M. E. Fisher, “Critical exponents in 3.993.993.993.99 dimensions”, Phys. Rev. Lett. 28 (1972) 240. [10.1103/PhysRevLett.28.240]
  2. J. C. Le Guillou and J. Zinn-Justin, “Accurate critical exponents for Ising like systems in noninteger dimensions”, J. Phys. (Les Ulis) 48 (1987) 19. [10.1016/B978-0-444-88597-5.50077-6]
  3. R. Guida and J. Zinn-Justin, “Critical exponents of the N𝑁Nitalic_N-vector model”, J. Phys. A 31 (1998) 8103. [10.1088/0305-4470/31/40/006]
  4. A. Pelissetto and E. Vicari, “Critical phenomena and renormalization group theory”, Phys. Rept. 368 (2002) 549. [10.1016/S0370-1573(02)00219-3]
  5. V. V. Prudnikov, P. V. Prudnikov and A. A. Fedorenko, “Field-theory approach to critical behavior of systems with long-range correlated defects”, Phys. Rev. B 62 (2000) 8777. [10.1103/PhysRevB.62.8777]
  6. C. Behan, L. Rastelli, S. Rychkov and B. Zan, “A scaling theory for the long-range to short-range crossover and an infrared duality”, J. Phys. A 50 (2017) 354002. [10.1088/1751-8121/aa8099]
  7. N. Defenu, A. Trombettoni and S. Ruffo, “Criticality and Phase Diagram of Quantum Long-Range O⁢(N)normal-O𝑁\mathrm{O}(N)roman_O ( italic_N ) models”, Phys. Rev. B 96 (2017) 104432. [10.1103/PhysRevB.96.104432]
  8. A. W. W. Ludwig, “Critical behavior of the two-dimensional random q𝑞qitalic_q-state Potts model by expansion in (q−2)𝑞2(q-2)( italic_q - 2 ), Nucl. Phys. B 285 (1987) 97–142. [10.1016/0550-3213(87)90330-0]
  9. J. L. Jacobsen, P. Le Doussal, M. Picco, R. Santachiara and K. J. Wiese, “Critical interfaces in the random-bond Potts model”, Phys. Rev. Lett. 102 (2009) 070601. [10.1103/PhysRevLett.102.070601]
  10. Z. Komargodski and D. Simmons-Duffin, “The Random-Bond Ising Model in 2.012.012.012.01 and 3333 Dimensions”, J. Phys. A 50 (2017) 154001. [10.1088/1751-8121/aa6087]
  11. G. Parisi and N. Sourlas, “Random magnetic fields, supersymmetry, and negative dimensions”, Phys. Rev. Lett. 43 (1979) 744. [10.1103/PhysRevLett.43.744]
  12. A. Kaviraj, S. Rychkov and E. Trevisani, “Parisi–Sourlas Supersymmetry in Random Field Models”, Phys. Rev. Lett. 129 (2022) 045701. [0.1103/PhysRevLett.129.045701]
  13. K. J. Wiese, “Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles”, Rep. Prog. Phys. 85 (2022) 086502. [10.1088/1361-6633/ac4648]
  14. R. Rattazzi, V. S. Rychkov, E. Tonni and A. Vichi, “Bounding scalar operator dimensions in 4⁢D4𝐷4D4 italic_D CFT”, JHEP 0812 (2008) 031. [10.1088/1126-6708/2008/12/031]
  15. S. El-Showk, M. F. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, “Solving the 3⁢d3𝑑3d3 italic_d Ising Model with the Conformal Bootstrap II. c𝑐citalic_c-Minimization and Precise Critical Exponents”, J. Stat. Phys. 157 (2014) 869. [10.1103/PhysRevD.86.025022]
  16. D. Poland, S. Rychkov and A. Vichi, “The Conformal Bootstrap: Theory, Numerical Techniques, and Applications”, Rev. Mod. Phys. 91 (2019) 015002. [10.1103/RevModPhys.91.015002]
  17. S. El-Showk, M. Paulos, D. Poland, S. Rychkov, D. Simmons-Duffin and A. Vichi, “Conformal Field Theories in Fractional Dimensions”, Phys. Rev. Lett. 112 (2014) 141601. [10.1103/PhysRevLett.112.141601]
  18. B. Sirois, “Navigating through the O⁢(N)normal-O𝑁\mathrm{O}(N)roman_O ( italic_N ) archipelago”, SciPost Phys. 13 (2022) no. 4, 081. [10.21468/SciPostPhys.13.4.081]
  19. C. Behan, “PyCFTBoot: A flexible interface for the conformal bootstrap”, Commun. Comput. Phys. 22 (2017) no. 1, 1 – 38. [10.4208/cicp.OA-2016-0107]
  20. A. Cappelli, L. Maffi and S. Okuda, “Critical Ising Model in Varying Dimension by Conformal Bootstrap”, JHEP 01 (2019) 161. [10.1007/JHEP01(2019)161]
  21. J.  Henriksson, S. R. Kousvos, M. Reehorst, “Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite ϵitalic-ϵ\epsilonitalic_ϵ”, JHEP 02 (2023), 218. [10.1007/JHEP02(2023)218]
  22. A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, “Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory”, Nucl. Phys. B 241 (1984) 333. [10.1016/0550-3213(84)90052-X]
  23. P. Di Francesco, P. Mathieu and D. Senechal, “Conformal Field Theory”, Springer-Verlag, New York (1997), 978-1-4612-2256-9. [10.1007/978-1-4612-2256-9]
  24. S. Rychkov and Z. M. Tan, “The ϵitalic-ϵ\epsilonitalic_ϵ-yexpansion from conformal field theory”, J. Phys. A 48 (2015) 29FT01. [10.1088/1751-8113/48/29/29FT01]
  25. F. Gliozzi, A. L. Guerrieri, A. C. Petkou and C. Wen, “The analytic structure of conformal blocks and the generalized Wilson–Fisher fixed points”, JHEP 1704 (2017) 056. [10.1007/JHEP04(2017)056]
  26. L. F. Alday, “Large Spin Perturbation Theory for Conformal Field Theories”, Phys. Rev. Lett. 119 (2017) 111601. [10.1103/PhysRevLett.119.111601]
  27. L. F. Alday, J. Henriksson and M. van Loon, “Taming the ϵitalic-ϵ\epsilonitalic_ϵ-expansion with large spin perturbation theory”, JHEP 1807 (2018) 131. [10.1007/JHEP07(2018)131]
  28. A. Bissi, A. Sinha and X. Zhou, “Selected Topics in Analytic Conformal Bootstrap: A Guided Journey”, Phys. Rept. 991 (2022), 1 – 89. [10.1016/j.physrep.2022.09.004]
  29. T. Hartman, D. Mazac, D. Simmons-Duffin and A. Zhiboedov, “Snowmass White Paper: The Analytic Conformal Bootstrap”. [10.48550/arXiv.2202.11012]
  30. F. Bertucci, J. Henriksson and B. McPeak, “Analytic bootstrap of mixed correlators in the O⁢(n)normal-O𝑛\mathrm{O}(n)roman_O ( italic_n ) CFT”, JHEP 10 (2022), 104. [10.1007/JHEP10(2022)104]
  31. J. Henriksson, “The critical O⁢(N)normal-O𝑁\mathrm{O}(N)roman_O ( italic_N ) CFT: Methods and conformal data”, Phys. Rept. 1002 (2023), 1-72. [10.1016/j.physrep.2022.12.002]
  32. J. Henriksson and M. Van Loon, “Critical O⁢(N)normal-O𝑁\mathrm{O}(N)roman_O ( italic_N ) model to order ϵ4superscriptitalic-ϵ4\epsilon^{4}italic_ϵ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT from analytic bootstrap”, J. Phys. A 52 (2019) 025401. [10.1088/1751-8121/aaf1e2]
  33. M. Hogervorst, S. Rychkov and B. C. van Rees, “Unitarity violation at the Wilson–Fisher fixed point in 4−ϵ4italic-ϵ4-\epsilon4 - italic_ϵ dimensions”, Phys. Rev. D 93 (2016) 125025. [10.1103/PhysRevD.93.125025]
  34. D. Simmons-Duffin, “A Semidefinite Program Solver for the Conformal Bootstrap”, JHEP 1506 (2015) 174. [10.1007/JHEP06(2015)174]
  35. S. El-Showk and M. F. Paulos, “Bootstrapping Conformal Field Theories with the Extremal Functional Method”, Phys. Rev. Lett. 111 (2013) 241601. [10.1103/PhysRevLett.111.241601]
  36. S. El-Showk and M. F. Paulos, “Extremal bootstrapping: go with the flow”, JHEP 1803 (2018) 148. [10.1007/JHEP03(2018)148]
  37. M. Reehorst, S. Rychkov, D. Simmons-Duffin, B. Sirois, N. Su and B. van Rees, “Navigator Function for the Conformal Bootstrap”, SciPost Phys. 11 (2021) 072. [10.21468/SciPostPhys.11.3.072]
  38. M. Kompaniets, “Prediction of the higher-order terms based on Borel resummation with conformal mapping”, J. Phys. Conf. Ser. 762 (2016) 012075. [10.1088/1742-6596/762/1/012075]
  39. D. V. Batkovich, K. G. Chetyrkin and M. V. Kompaniets, “Six loop analytical calculation of the field anomalous dimension and the critical exponent η𝜂\etaitalic_η in O⁢(n)normal-O𝑛\mathrm{O}(n)roman_O ( italic_n )-symmetric φ4superscript𝜑4\varphi^{4}italic_φ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT model”, Nucl. Phys. B 906 (2016) 147. [10.1016/j.nuclphysb.2016.03.009]
  40. M. V. Kompaniets and E. Panzer, “Minimally subtracted six loop renormalization of O⁢(n)normal-O𝑛\mathrm{O}(n)roman_O ( italic_n )-symmetric ϕ4superscriptitalic-ϕ4\phi^{4}italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT theory and critical exponents”, Phys. Rev. D 96 (2017) 036016. [10.1103/PhysRevD.96.036016]
  41. M. V. Kompaniets and K. J. Wiese, “Fractal dimension of critical curves in the O⁢(n)normal-O𝑛\mathrm{O}(n)roman_O ( italic_n )-symmetric ϕ4superscriptitalic-ϕ4\phi^{4}italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT model and crossover exponent at 6666-loop order: Loop-erased random walks, self-avoiding walks, Ising, XY, and Heisenberg models”, Phys. Rev. E 101 (2020) 012104. [10.1103/PhysRevE.101.012104]
  42. M. Hasenbusch, “Finite size scaling study of lattice models in the three-dimensional Ising universality class”, Phys. Rev. B 82 (2010) 174433. [10.1103/PhysRevB.82.174433]
  43. A. M. Ferrenberg, J. Xu and D. P. Landau, “Pushing the limits of monte carlo simulations for the three-dimensional Ising model, Phys. Rev. E 97 (2018) 043301. [10.1103/PhysRevE.97.043301]
  44. M. Hasenbusch, “Restoring isotropy in a three-dimensional lattice model: The Ising universality class”, Phys. Rev. B 104 (2021) 014426. [10.1103/PhysRevB.104.014426]
  45. I. Balog, H. Chaté, B. Delamotte, M. Marohnic and N. Wschebor, “Convergence of Nonperturbative Approximations to the Renormalization Group”, Phys. Rev. Lett. 123 (2019) 240604. [10.1103/PhysRevLett.123.240604]
  46. N. Dupuis, L. Canet, A. Eichhorn, W. Metzner, J.M. Pawlowski, M. Tissier and N. Wschebor, “The nonperturbative functional renormalization group and its applications, Phys. Rep. 910 (2021) 1. [10.1016/j.physrep.2021.01.001]
  47. F. Kos, D. Poland and D. Simmons-Duffin, “Bootstrapping Mixed Correlators in the 3⁢D3𝐷3D3 italic_D Ising Model”, JHEP 1411 (2014) 109. [10.1007/JHEP11(2014)109]
  48. D. Simmons-Duffin, “The Lightcone Bootstrap and the Spectrum of the 3⁢d3𝑑3d3 italic_d Ising CFT”, JHEP 1703 (2017) 086. [10.1103/PhysRevD.86.025022]
  49. G. A. F. Seber and A. J. Lee, “Linear Regression Analysis” (Second ed.), John Wiley & Sons, Inc., Hoboken, New Jersey (2003), 978-0471415404. [10.1002/9780471722199]
  50. M. Reehorst, “Rigorous bounds on irrelevant operators in the 3⁢d3𝑑3d3 italic_d Ising model CFT”, JHEP 09 (2022) 177. [10.1007/JHEP09(2022)177]
  51. J. Zinn-Justin, “Quantum Field Theory and Critical Phenomena” (Fourth ed.), Clarendon Press, Oxford (2002), 978-0198509233. [10.1002/qua.560460607]
  52. A. N. Vasiliev, “The field theoretic renormalization group in critical behavior theory and stochastic dynamics”, Chapman & Hall/CRC, Boca Raton (2004), 9780429204555. [10.1201/9780203483565]
  53. O. Schnetz, “Numbers and Functions in Quantum Field Theory”, Phys. Rev. D 97 (2018) 085018. [10.1103/PhysRevD.97.085018]
  54. G. V. Dunne and M. Meynig, “Instantons or renormalons? Remarks on ϕd=44superscriptsubscriptitalic-ϕ𝑑44\phi_{d=4}^{4}italic_ϕ start_POSTSUBSCRIPT italic_d = 4 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT theory in the MS scheme”, Phys. Rev. D 105 (2022) 025019. [PhysRevD.105.025019]
  55. I. Aniceto, G. Basar and R. Schiappa, “A Primer on Resurgent Transseries and Their Asymptotics”, Phys. Rept. 809 (2019) 1. [10.1016/j.physrep.2019.02.003]
  56. H. Mera, T. G. Pedersen and B. K. Nikolić, “Fast summation of divergent series and resurgent transseries from Meijer-G approximants”, Phys. Rev. D 97 (2018) 105027. [10.1103/PhysRevD.97.105027]
  57. G. Sberveglieri, M. Serone and G. Spada, “Renormalization scheme dependence, RG flow, and Borel summability in ϕ4superscriptitalic-ϕ4\phi^{4}italic_ϕ start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT Theories in d<4𝑑4d<4italic_d < 4”, Phys. Rev. D 100 (2019) 045008. [10.1103/PhysRevD.100.045008]
  58. R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, “Conformal Bootstrap in Mellin Space”, Phys. Rev. Lett. 118 (2017) 081601. [10.1103/PhysRevLett.118.081601]
  59. R. Gopakumar, A. Kaviraj, K. Sen and A. Sinha, “A Mellin space approach to the conformal bootstrap”, JHEP 1705 (2017) 027. [10.1007/JHEP05(2017)027]
  60. S. E. Derkachov and A. N. Manashov, “On the stability problem in the O⁢(N)normal-O𝑁\mathrm{O}(N)roman_O ( italic_N ) nonlinear sigma model”, Phys. Rev. Lett. 79 (1997) 1423. [10.1103/PhysRevLett.79.1423]
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