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.
Article PDF
Similar content being viewed by others
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).
Author information
Authors and Affiliations
Additional information
Fiz. Tverd. Tela (St. Petersburg) 40, 1284–1290 (July 1998)
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1134/1.1130512