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Critical indices from self-similar root approximants

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Abstract.

The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now this method is generalized for the purpose of extrapolating small-variable expansions to the region of finite and large variables, where the sought function exhibits critical behaviour. The procedure of calculating critical indices is formulated and illustrated by a variety of physical problems.

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References

  1. G.A. Baker, P. Graves-Moris, Padé Approximants (Cambridge University, Cambridge, 1996)

  2. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics and Financial Markets (World Scientific, Singapore, 2006)

  3. S. Gluzman, V.I. Yukalov, Eur. J. Appl. Math. 25, 595 (2014)

    Article  Google Scholar 

  4. S. Gluzman, V.I. Yukalov, Eur. Phys. J. Plus 131, 340 (2016)

    Article  Google Scholar 

  5. V.I. Yukalov, Phys. Rev. 42, 3324 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  6. V.I. Yukalov, J. Math. Phys. 32, 1235 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  7. V.I. Yukalov, J. Math. Phys. 33, 3994 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  8. V.I. Yukalov, S. Gluzman, Phys. Rev. Lett. 79, 333 (1997)

    Article  ADS  Google Scholar 

  9. S. Gluzman, V.I. Yukalov, Phys. Rev. E 58, 4197 (1998)

    Article  ADS  Google Scholar 

  10. V.I. Yukalov, E.P. Yukalova, S. Gluzman, Phys. Rev. A 58, 96 (1998)

    Article  ADS  Google Scholar 

  11. V.I Yukalov, E.P. Yukalova, S. Gluzman, J. Math. Chem. 47, 959 (2010)

    Article  MathSciNet  Google Scholar 

  12. S. Gluzman, V.I. Yukalov, J. Math. Chem. 48, 883 (2010)

    Article  MathSciNet  Google Scholar 

  13. S. Gluzman, V.I. Yukalov, Mathematics 3, 510 (2015)

    Article  Google Scholar 

  14. V.I. Yukalov, S. Gluzman, Phys. Rev. D 91, 125023 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. V.L. Kalitvyansky, A.P. Kashin, M.Z. Maximov, Z.E. Chikovani, J. Nucl. Phys. 41, 329 (1985)

    Google Scholar 

  16. H.X. He, C.J. Hamer, J. Oitmaa, J. Phys. A 23, 1775 (1990)

    Article  ADS  Google Scholar 

  17. R.J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London, 1982)

  18. P. Butera, M. Comi, J. Stat. Phys. 109, 311 (2002)

    Article  Google Scholar 

  19. H. Kleinert, V. Schulte-Frohlinde, Critical Properties of $\varphi^{4}$-Theories (World Scientific, Singapore, 2006)

  20. G.K. Batchelor, J.T. Green, J. Fluid Mech. 56, 401 (1972)

    Article  ADS  Google Scholar 

  21. E. Wajnryb, J.S. Dahler, Adv. Chem. Phys. 102, 193 (1997)

    Google Scholar 

  22. B. Cichocki, M.L. Ekiel-Jezewska, E. Wajnryb, J. Chem. Phys. 119, 606 (2003)

    Article  ADS  Google Scholar 

  23. D. Stauffer, A. Coniglio, M. Adam, Adv. Polymer Sci. 44, 103 (1982)

    Article  Google Scholar 

  24. T.M. Nieuwenhuizen, P.F.J. van Velthoven, M.H. Ernst, Phys. Rev. Lett. 57, 2477 (1986)

    Article  ADS  Google Scholar 

  25. D. Frenkel, Phys. Lett. A 121, 385 (1987)

    Article  ADS  Google Scholar 

  26. P. Grassberger, Physica A 262, 251 (1999)

    Article  ADS  Google Scholar 

  27. S. Kirkpatrick, Rev. Mod. Phys. 45, 574 (1973)

    Article  ADS  Google Scholar 

  28. F. Hofling, T. Franosch, E. Frey, Phys. Rev. Lett. 96, 165901 (2006)

    Article  ADS  Google Scholar 

  29. T. Bauer, F. Hofling, T. Munk, E. Frey, T. Franosch, Eur. Phys. J. ST 189, 103 (2010)

    Article  Google Scholar 

  30. P.M. Adler, Porous Media. Geometry and Transport (Batterworth-Heinemann, Oxford, 1992)

  31. A.E. Malevich, V.V. Mityushev, P.M. Adler, Acta Mech. 182, 151 (2006)

    Article  Google Scholar 

  32. J. Cioslowski, J. Chem. Phys. 136, 044109 (2012)

    Article  ADS  Google Scholar 

  33. E. Matito, J. Cioslowski, S.F. Vyboishchikov, Phys. Chem. Chem. Phys. 12, 6712 (2010)

    Article  Google Scholar 

  34. A. Mulero, Theory and Simulation of Hard-Sphere Fluids and Related Systems (Springer, Berlin, 2008)

  35. G.W. Wu, R.J. Sadus, Am. Inst. Chem. Eng. J. 51, 309 (2005)

    Article  Google Scholar 

  36. J. Tian, H. Jiang, Y. Gui, A. Mulero, Phys. Chem. Chem. Phys. 11, 11213 (2009)

    Article  Google Scholar 

  37. J. Tian, Y. Gui, A. Mulero, J. Phys. Chem. B 114, 13399 (2010)

    Article  Google Scholar 

  38. X.Z. Wang, H.R. Ma, Chin. J. Chem. Phys. 23, 675 (2010)

    Article  Google Scholar 

  39. M. Muthukumar, B.G. Nickel, J. Chem. Phys. 80, 5839 (1984)

    Article  ADS  Google Scholar 

  40. M. Muthukumar, B.G. Nickel, J. Chem. Phys. 86, 460 (1987)

    Article  ADS  Google Scholar 

  41. B. Li, N. Madras, A.D. Sokal, J. Stat. Phys. 80, 661 (1995)

    Article  ADS  Google Scholar 

  42. G.K. Batchelor, J. Fluid Mech. 52, 245 (1972)

    Article  ADS  Google Scholar 

  43. C.W.J. Beenakker, P. Mazur, Physica A 120, 388 (1984)

    Article  ADS  Google Scholar 

  44. J.F. Brady, L.J. Durlofsky, Phys. Fluids 31, 717 (1988)

    Article  ADS  Google Scholar 

  45. A.J.C. Ladd, J. Chem. Phys. 93, 3484 (1990)

    Article  ADS  Google Scholar 

  46. H. Hayakawa, K. Ichiki, Phys. Rev. E 51, 3815 (1995)

    Article  ADS  Google Scholar 

  47. B. Cichocki, M.L. Ekiel-Jezewska, P. Szymczak, E. Wajnryb, J. Chem. Phys. 117, 1231 (2002)

    Article  ADS  Google Scholar 

  48. J. Schwinger, Phys. Rev. 128, 2425 (1962)

    Article  ADS  MathSciNet  Google Scholar 

  49. T. Banks, L. Susskind, J. Kogut, Phys. Rev. D 13, 1043 (1976)

    Article  ADS  Google Scholar 

  50. P. Striganesh, C.J. Hamer, R.J. Bursill, Phys. Rev. D 62, 034508 (2000)

    Article  ADS  Google Scholar 

  51. S. Coleman, Ann. Phys. (N.Y.) 101, 239 (1976)

    Article  ADS  Google Scholar 

  52. C.J. Hamer, Nucl. Phys. B 121, 159 (1977)

    Article  ADS  Google Scholar 

  53. C.J. Hamer, Z. Weihong, J. Oitmaa, Phys. Rev. D 56, 55 (1997)

    Article  ADS  Google Scholar 

  54. A. Carrol, J. Kogut, D.K. Sinclair, L. Susskind, Phys. Rev. D 13, 2270 (1976)

    Article  ADS  Google Scholar 

  55. J.P. Vary, T.J. Fields, H.J. Pirner, Phys. Rev. D 53, 7231 (1996)

    Article  ADS  Google Scholar 

  56. C. Adam, Phys. Lett. B 382, 383 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  57. U. Seifert, Adv. Phys 46, 13 (1997)

    Article  ADS  Google Scholar 

  58. G. Gompper, D.M. Kroll, Europhys. Lett. 9, 59 (1989)

    Article  ADS  Google Scholar 

  59. B. Kastening, Phys. Rev. E 73, 011101 (2006)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia

    S. Gluzman & V. I. Yukalov

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  1. S. Gluzman
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  2. V. I. Yukalov
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Correspondence to V. I. Yukalov.

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Gluzman, S., Yukalov, V.I. Critical indices from self-similar root approximants. Eur. Phys. J. Plus 132, 535 (2017). https://doi.org/10.1140/epjp/i2017-11820-2

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