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R. Schloms; V. Dohm

doi:10.1103/PhysRevB.42.6142

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Minimal renormalization without ε expansion: Critical behavior above and below $T_{c}$

R. Schloms and V. Dohm

Institut für Theoretische Physik, Technische Hochschule Aachen, D-5100 Aachen, Federal Republic of Germany

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Phys. Rev. B 42, 6142 – Published 1 October, 1990Erratum Phys. Rev. B 46, 5883 (1992)

DOI: https://doi.org/10.1103/PhysRevB.42.6142

Abstract

We present a field-theoretic renormalization-group treatment of the critical behavior of the ${cphi}^{4}$ model within the minimal-subtraction scheme at fixed dimension d<4. We show that correlation functions above and below $T_{c}$ can be calculated within this renormalization scheme without using the ε=4-d expansion. This is demonstrated for the specific heat, for the order parameter, and for the superfluid density (stiffness constant). Various asymptotic amplitudes and correction amplitudes are determined, and some of their universal ratios are calculated in three dimensions. Our result for $a_{c}^{-}$ / $a_{ρ s}$ eliminates a previous error of the ε expansion regarding the sign of this ratio for d=3 and n=2.

Erratum

Erratum: Minimal renormalization without $ε$ expansion: Critical behavior above and below $T_{c}$

R. Schloms and V. Dohm

Phys. Rev. B 46, 5883 (1992)

References (40)

G. t'Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972); G. t'Hooft, ibid. 61, 455 (1973).
D. J. Amit, Field Theory, the Renormalization Group and Critical Phenomena (McGraw-Hill, New York, 1978).
R. Schloms and V. Dohm, Nucl. Phys. B 328, 639 (1989).
K. Symanzik, Lett. Nuovo Cimento 8, 71 (1973).
V. Dohm, Z. Phys. B 60, 61 (1985).
R. Schloms and V. Dohm, Europhys. Lett. 3, 413 (1987).
C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978).
V. Dohm, J. Low Temp. Phys. 69, 51 (1987).
J. Pankert and V. Dohm, Europhys. Lett. 2, 775 (1986); Phys. Rev. B 40, 10842 (1989) ibid. 40, 10856 (1989).
W. Huhn and V. Dohm, Phys. Rev. Lett. 61, 1368 (1988).
J. Eggers and V. Dohm (unpublished).
H. W. Diehl, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1986), Vol. 10.
D. Frank and V. Dohm, Phys. Rev. Lett. 62, 1864 (1989).
J. Zinn-Justin, Phys. Rep. 70, 109 (1981).
H. J. Krause, R. Schloms and V. Dohm, Z. Phys. B 79, 287 (1990); ibid. 80, 313 (1990).
C. Bagnuls and C. Bervillier, Phys. Rev. B 27, 6995 (1983); ibid. 32, 7209 (1985).
C. Bagnuls, C. Bervillier, D. I. Meiron and B. G. Nickel, Phys. Rev. B 35, 3585 (1987).
V. Dohm, Phys. Rev. Lett. 53, 1379, 2520 (1984).
R. Schloms, J. Eggers, and V. Dohm, Jpn. J. Appl. Phys. Suppl. 26-3, 49 (1987).
D. S. Greywall and G. Ahlers, Phys. Rev. Lett. 28, 1251 (1972).
G. Ahlers, Phys. Rev. A 3, 696 (1971); ibid. 8, 530 (1973).
A. Singsaas and G. Ahlers, Phys. Rev. B 30, 5103 (1984).
W. Y. Tam and G. Ahlers, Phys. Rev. B 32, 5932 (1985); ibid. 33, 183 (1986); ibid. 37, 7898 (1988).
V. Dohm, Z. Phys. B 61, 193 (1985).
E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6.
C. Bagnuls and C. Bervillier, Phys. Lett. 107A, 299 (1985).
B. I. Halperin, P. C. Hohenberg and S. K. Ma, Phys. Rev. B 10, 139 (1974).
I. D. Lawrie, J. Phys. A 18, 1141 (1985).
P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) 34, 291 (1965).
B. D. Josephson, Phys. Lett. 21, 608 (1966).
B. I. Halperin and P. C. Hohenberg, Phys. Rev. 177, 952 (1969); P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
See, e.g., the articles in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. VI.
V. Privman, P. C. Hohenberg, and A. Aharony (unpublished).
F. Wegner, Phys. Rev. B 5, 4529 (1972).
J. C. Le Guillou and J. Zinn-Justin, J. Phys. Lett. (Paris) 46, 137 (1985).
M. Barmatz, P. C. Hohenberg and A. Kornblit, Phys. Rev. B 12, 1947 (1975).
S. I. Chase and M. Kaufman, Phys. Rev. B 33, 239 (1986).
C. Bervillier, Phys. Rev. B 34, 8141 (1986).
A. Aharony and G. Ahlers, Phys. Rev. Lett. 44, 782 (1980); M. C. Chang and A. Houghton, ibid. 44, 785 (1980).
M. C. Chang and A. Houghton, Phys. Rev. B 23, 1473 (1981).

[c1] G. t'Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972); G. t'Hooft, ibid. 61, 455 (1973).

[c2] D. J. Amit, Field Theory, the Renormalization Group and Critical Phenomena (McGraw-Hill, New York, 1978).

[c3] R. Schloms and V. Dohm, Nucl. Phys. B 328, 639 (1989).

[c4] K. Symanzik, Lett. Nuovo Cimento 8, 71 (1973).

[c5] V. Dohm, Z. Phys. B 60, 61 (1985).

[c6] R. Schloms and V. Dohm, Europhys. Lett. 3, 413 (1987).

[c7] C. De Dominicis and L. Peliti, Phys. Rev. B 18, 353 (1978).

[c8] V. Dohm, J. Low Temp. Phys. 69, 51 (1987).

[c9] J. Pankert and V. Dohm, Europhys. Lett. 2, 775 (1986); Phys. Rev. B 40, 10842 (1989) ibid. 40, 10856 (1989).

[c10] W. Huhn and V. Dohm, Phys. Rev. Lett. 61, 1368 (1988).

[c11] J. Eggers and V. Dohm (unpublished).

[c12] H. W. Diehl, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, New York, 1986), Vol. 10.

[c13] D. Frank and V. Dohm, Phys. Rev. Lett. 62, 1864 (1989).

[c14] J. Zinn-Justin, Phys. Rep. 70, 109 (1981).

[c15] H. J. Krause, R. Schloms and V. Dohm, Z. Phys. B 79, 287 (1990); ibid. 80, 313 (1990).

[c16] C. Bagnuls and C. Bervillier, Phys. Rev. B 27, 6995 (1983); ibid. 32, 7209 (1985).

[c17] C. Bagnuls, C. Bervillier, D. I. Meiron and B. G. Nickel, Phys. Rev. B 35, 3585 (1987).

[c18] V. Dohm, Phys. Rev. Lett. 53, 1379, 2520 (1984).

[c19] R. Schloms, J. Eggers, and V. Dohm, Jpn. J. Appl. Phys. Suppl. 26-3, 49 (1987).

[c20] D. S. Greywall and G. Ahlers, Phys. Rev. Lett. 28, 1251 (1972).

[c21] G. Ahlers, Phys. Rev. A 3, 696 (1971); ibid. 8, 530 (1973).

[c22] A. Singsaas and G. Ahlers, Phys. Rev. B 30, 5103 (1984).

[c23] W. Y. Tam and G. Ahlers, Phys. Rev. B 32, 5932 (1985); ibid. 33, 183 (1986); ibid. 37, 7898 (1988).

[c24] V. Dohm, Z. Phys. B 61, 193 (1985).

[c25] E. Brézin, J. C. Le Guillou, and J. Zinn-Justin, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6.

[c26] C. Bagnuls and C. Bervillier, Phys. Lett. 107A, 299 (1985).

[c27] B. I. Halperin, P. C. Hohenberg and S. K. Ma, Phys. Rev. B 10, 139 (1974).

[c28] I. D. Lawrie, J. Phys. A 18, 1141 (1985).

[c29] P. C. Hohenberg and P. C. Martin, Ann. Phys. (N.Y.) 34, 291 (1965).

[c30] B. D. Josephson, Phys. Lett. 21, 608 (1966).

[c31] B. I. Halperin and P. C. Hohenberg, Phys. Rev. 177, 952 (1969); P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).

[c32] See, e.g., the articles in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. VI.

[c33] V. Privman, P. C. Hohenberg, and A. Aharony (unpublished).

[c34] F. Wegner, Phys. Rev. B 5, 4529 (1972).

[c35] J. C. Le Guillou and J. Zinn-Justin, J. Phys. Lett. (Paris) 46, 137 (1985).

[c36] M. Barmatz, P. C. Hohenberg and A. Kornblit, Phys. Rev. B 12, 1947 (1975).

[c37] S. I. Chase and M. Kaufman, Phys. Rev. B 33, 239 (1986).

[c38] C. Bervillier, Phys. Rev. B 34, 8141 (1986).

[c39] A. Aharony and G. Ahlers, Phys. Rev. Lett. 44, 782 (1980); M. C. Chang and A. Houghton, ibid. 44, 785 (1980).

[c40] M. C. Chang and A. Houghton, Phys. Rev. B 23, 1473 (1981).

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Minimal renormalization without ε expansion: Critical behavior above and below $T_{c}$

Abstract

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Erratum: Minimal renormalization without $ε$ expansion: Critical behavior above and below $T_{c}$

References (40)

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Minimal renormalization without ε expansion: Critical behavior above and below Tc

Abstract

Erratum

Erratum: Minimal renormalization without ε expansion: Critical behavior above and below Tc

References (40)

Minimal renormalization without ε expansion: Critical behavior above and below $T_{c}$

Erratum: Minimal renormalization without $ε$ expansion: Critical behavior above and below $T_{c}$