Abstract
The aim of this study is to find universal critical values of the effective dimensionless coupling constant g 6 and refined universal values g 4 for Heisenberg ferromagnets with n-component order parameters. These constants appear in the equation of state and determine the nonlinear susceptibilities χ 4 and χ 6 in the critical region. Calculations are made of the first three terms of the expansion of g 6 in powers of g 4 in the limits of O(n) symmetry three-dimensional λϕ 4 theory, the resultant series is resummed by the Padé-Borel method, and then by substituting the fixed point coordinates g *4 in the resultant expression, numerical values of g *6 are obtained for different n. These numbers g *4 for n>3 were determined from a six-loop expansion for the β-function resummed using the Padé-Borel-Leroy technique. An analysis of the accuracy of these g *6 values showed that they may differ from the true values by no more than 1.6%. These values of g *6 were compared with those obtained by the 1/n expansion method which allowed the level of accuracy of this method to be assessed.
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References
N. D. Mermin and G. Stare, Phys. Rev. Lett. 30, 1135 (1973).
A. I. Sokolov, Zh. Éksp. Teor. Fiz. 78, 1985 (1980) [Sov. Phys. JETP 51, 998 (1980)].
J. A. Sauls and J. W. Serene, Phys. Rev. D 17, 1524 (1978).
A. I. Sokolov, Zh. Éksp. Teor. Fiz. 79, 1137 (1980) [Sov. Phys. JETP 52, 1137 (1980)].
F. Wilczek, Int. J. Mod. Phys. A 7, 3911 (1992).
K. Rajagopal and F. Wilczek, Nucl. Phys. B 399, 395 (1993).
G. A. Baker, B. G. Nickel, and D. I. Meiron, Phys. Rev. B 17, 1365 (1978).
J. C. Le Guillou and J. Zinn-Justin, Phys. Rev. Lett. 39, 95 (1977).
S. A. Antonenko and A. I. Sokolov, Phys. Rev. E 51, 1894 (1995).
C. Bagnuls and C. Bervillier, Phys. Rev. B 41, 402 (1990).
N. Tetradis and C. Wetterich, Nucl. Phys. B 422, 541 (1994).
M. M. Tsypin, Phys. Rev. Lett. 73, 2015 (1994).
T. Reisz, Phys. Lett. B 360, 77 (1995).
A. I. Sokolov, Fiz. Tverd. Tela (St. Petersburg) 38, 640 (1996) [Phys. Solid State 38, 354 (1996)].
S. Y. Zinn, S. N. Lai, and M. E. Fisher, Phys. Rev. E 54, 1176 (1996).
A. I. Sokolov, V. A. Ul’kov, and E. V. Orlov, J. Phys. Studies 1, 362 (1997).
A. I. Sokolov, E. V. Orlov, and V. A. Ul’kov Phys. Lett. A 227, 255 (1997).
R. Guida and J. Zinn-Justin, Nucl. Phys. B 489, 626 (1997).
T. R. Morris, Nucl. Phys. B 495, 477 (1997).
P. Butera and M. Comi, Phys. Rev. E 55, 6391 (1997).
M. M. Tsypin, Phys. Rev. B 55, 8911 (1997).
G. A. Baker and N. Kawashima, Phys. Rev. Lett. 75, 994 (1995).
G. A. Baker and N. Kawashima, J. Phys. A 29, 7183 (1996).
A. I. Sokolov, Zh. Éksp. Teor. Fiz. 77, 1598 (1979) [Sov. Phys. JETP 50, 802 (1979)].
B. G. Nickel, D. I. Meiron, and G. A. Baker, Jr., Compilation of 2-pt and 4-pt graphs for continuous spin model, University of Guelph Report, 1977 (unpublished).
G. A. Baker, Jr. and P. Graves-Morris, Padé Approximants, Parts 1 and 2 (Addison-Wesley, Reading, Mass, 1981; Mir, Moscow, 1986).
S. Goldner and G. Ahlers Phys. Rev. B 45, 13 129 (1992).
J. A. Lipa, D. R. Swanson, J. A. Nissen, T. C. P. Chui, and U. E. Israelsson, Phys. Rev. Lett. 76, 944 (1996).
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Fiz. Tverd. Tela (St. Petersburg) 40, 1284–1290 (July 1998)
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Sokolov, A.I. Universal effective coupling constants for the generalized Heisenberg model. Phys. Solid State 40, 1169–1174 (1998). https://doi.org/10.1134/1.1130512
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DOI: https://doi.org/10.1134/1.1130512