Abstract
The leading correction-to-scaling exponent ω for the three-dimensional (3D) dilute Ising model is calculated in the framework of the field theoretic renormalization group approach. Both in the minimal subtraction scheme and in the massive field theory (resummed four-loop expansion) excellent agreement with recent Monte Carlo calculations (H. G. Ballesteros et al., Phys. Rev. B 58, 2740 (1998)) is achieved. The expression of ω as a series in a \(\sqrt \varepsilon \) expansion up to O(ɛ2) does not permit a reliable estimate for d=3.
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References
F. J. Wegner, Phys. Rev. B 5, 4529 (1972).
H. Kleinert and V. Schulte-Frohlinde, Phys. Lett. B 342, 284 (1995).
A. B. Harris, J. Phys. C 7, 1671 (1974).
J. T. Chayes, L. Chayes, D. S. Fisher et al., Phys. Rev. Lett. 57, 2999 (1986).
D. P. Landau, Phys. Rev. B 22, 2450 (1980); J. Marro, A. Labarta, and J. Tejada, Phys. Rev. B 34, 347 (1986).
J.-S. Wang and D. Chowdhury, J. Phys. France 50, 2905 (1989); J.-S. Wang, M. Wohlert, H. Muhlenbein et al., Physica A 166, 173 (1990); H.-O. Heuer, Europhys. Lett. 12, 551 (1990); H.-O. Heuer, Phys. Rev. B 42, 6476 (1990); H.-O. Heuer, J. Phys. A 26, L333 (1993).
H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor et al., Phys. Rev. B 58, 2740 (1998).
S. Wiseman and E. Domany, Phys. Rev. Lett. 81, 22 (1998); Phys. Rev. E 58, 2938 (1998).
K. E. Newman and E. K. Riedel, Phys. Rev. B 25, 264 (1982).
J. Jug, Phys. Rev. B 27, 609 (1983).
H. K. Janssen, K. Oerding, and E. Sengespeick, J. Phys. A 28, 6073 (1995).
G. Grinstein and A. Luther, Phys. Rev. B 13, 1329 (1976); T. C. Lubensky, Phys. Rev. B 11, 3573 (1975).
G. Parisi, Proceedings of the Cargèse Summer School 1973 (unpublished); J. Stat. Phys. 23, 49 (1980).
G. t’Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972).
R. Schloms and V. Dohm, Europhys. Lett. 3, 413 (1987); Nucl. Phys. B 328, 639 (1989).
I. O. Mayer, A. I. Sokolov, and B. N. Shalaev, Ferroelectrics 95, 93 (1989); I. O. Mayer, J. Phys. A 22 2815 (1989).
G. B. Baker, B. G. Nickel, and D. I. Meiron, Phys. Rev. B 17, 1365 (1978).
H. Kleinert, J. Neu, V. Schulte-Frohlinde et al., Phys. Lett. B 272, 39 (1991); Phys. Lett. B 319, 545(E) (1993).
A. J. Bray, T. McCarthy, M. A. Moore et al., Phys. Rev. B 36, 2212 (1987); A. J. McKane, Phys. Rev. B 49, 12003 (1994).
P. J. S. Watson, J. Phys. A 7, L167 (1974).
J. S. R. Chisholm, Math. Comput. 27, 841 (1973).
R. Guida and J. Zinn-Justin, J. Phys. A 31, 8103 (1998).
C. F. Baillie, R. Gupta, K. A. Hawick et al., Phys. Rev. B 45, 10438 (1992).
H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor et al., J. Phys. A 32, 1 (1999).
R. Folk, Yu. Holovatch, and T. Yavors’kii, J. Phys. Stud. 2, 213 (1998) and unpublished.
A. Aharony, A. B. Harris, and S. Wiseman, Phys. Rev. Lett. 81, 252 (1998).
D. E. Khmel’nitskii, Zh. Éksp. Teor. Fiz. 68, 1960 (1975) [Sov. Phys. JETP 41, 981 (1975)].
B. N. Shalaev, S. A. Antonenko, and A. I. Sokolov, Phys. Lett. A 230, 105 (1997).
Up to O(ɛ) we recover the result of C. Jayaprakash and H. J. Katz, Phys. Rev. B 16, 3987 (1977), the \(\sqrt \varepsilon \) term is twice as large as in B. N. Shalaev, Zh. Éksp. Teor. Fiz. 73, 2301 (1977) [Sov. Phys. JETP 46, 1204 (1977)].
R. B. Griffith, Phys. Rev. Lett. 23, 17 (1969).
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Pis’ma Zh. Éksp. Teor. Fiz. 69, No. 10, 698–702 (25 May 1999)
Published in English in the original Russian journal. Edited by Steve Torstveit.