Influence of long-range interactions on the critical behavior of systems with a negative Fisher exponent

H. K. Janssen

doi:10.1103/PhysRevE.58.R2673

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Influence of long-range interactions on the critical behavior of systems with a negative Fisher exponent

H. K. Janssen

Institut für Theoretische Physik III, Heinrich-Heine-Universität, 40225 Düsseldorf, Germany

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Phys. Rev. E 58, R2673(R) – Published 1 September, 1998

DOI: https://doi.org/10.1103/PhysRevE.58.R2673

Abstract

The influence of long-range interactions decaying in d dimensions as ${1 / R}^{d + σ}$ on the critical behavior of systems with negativeFisher’s correlation-function exponent for short-range interactions, $η_{SR} < 0,$ is reexamined. Such systems, typically described by $φ^{3}$ -field theories, are, e.g., the Potts model in the percolation limit, the Edwards-Anderson spin-glass model, and the Yang-Lee edge singularity. In contrast to preceding studies, it is shown by means of Wilson’s momentum-shell renormalization-group recursion relations that the long-range interactions dominate as long as $σ < 2 - η_{SR} .$ Exponents change continuously to their short-range values at the boundary of this region.

References (19)

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W. K. Theumann and M. A. Gusmão, Phys. Rev. B 31, 379 (1985).
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N. Breuer and H. K. Janssen, Z. Phys. B 41, 55 (1981).
S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975).
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H. K. Janssen (unpublished).
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[c1] M.-c. Chang and J. Sak, Phys. Rev. B 29, 2652 (1984).

[c2] W. K. Theumann and M. A. Gusmão, Phys. Rev. B 31, 379 (1985).

[c3] M. E. Fisher, S.-k Ma, and B. G. Nickel, Phys. Rev. Lett. 29, 917 (1972).

[c4] J. Sak, Phys. Rev. B 8, 281 (1973).

[c5] A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6.

[c6] Y. Yamazaki, Nuovo Cimento A 55, 59 (1980).

[c7] J. Honkonen and M. Yu. Nalimov, J. Phys. A 22, 751 (1989).

[c8] F. J. Wegner, in Phase Transitions and Critical Phenomena (Ref. [5]).

[c9] O. F. de Alcantara Bonfim, J. E. Kirkham, and A. J. McKane, J. Phys. A 13, L247 (1980); ibid. 14, 2391 (1981).

[c10] A. B. Harris, T. C. Lubensky, W. K. Holcomb, and C. Dasgupta, Phys. Rev. Lett. 35, 327 (1975).

[c11] D. J. Amit, J. Phys. A 9, 1441 (1976).

[c12] R. G. Priest and T. C. Lubensky, Phys. Rev. B 13, 4159 (1976); ibid. 14, 5125(E) (1976).

[c13] M. E. Fisher, Phys. Rev. Lett. 40, 1610 (1978).

[c14] N. Breuer and H. K. Janssen, Z. Phys. B 41, 55 (1981).

[c15] S. F. Edwards and P. W. Anderson, J. Phys. F 5, 965 (1975).

[c16] A. B. Harris, T. C. Lubensky, and J.-H. Chen, Phys. Rev. Lett. 36, 415 (1976).

[c17] P. Grassberger, in Fractals in Physics, edited by L. Pietronero and E. Tosatti (Elsevier, New York, 1986).

[c18] H. K. Janssen (unpublished).

[c19] Z. Glumac and K. Uzelac, J. Phys. A 24, 501 (1991).

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Influence of long-range interactions on the critical behavior of systems with a negative Fisher exponent

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