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Volumn 63, Issue 5, 2001, Pages

Surface critical behavior of random systems: Ordinary transition

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; EXTRAPOLATION; PERTURBATION TECHNIQUES; SURFACE PHENOMENA;

EID: 0035335433     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.056102     Document Type: Article
Times cited : (13)

References (60)
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    • A. recent experimental review has been given in D. P. Belanger, e-print cond-mat/0009029.
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  • 18
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    • The three-loop beta functions derived and used in these articles are in error. The correct expressions for the RG functions of the relevant anisotropic mn-component model in three dimensions were obtained by one of the present authors in Ref. 18
    • Sov. Phys. Solid StateI. O. Maier, A. I. Sokolov, 26, 3454 (1984) [ 26, 2076 (1984)]. The three-loop beta functions derived and used in these articles are in error. The correct expressions for the RG functions of the relevant anisotropic mn-component model in three dimensions were obtained by one of the present authors in Ref. 18.
    • (1984) Sov. Phys. Solid State , vol.26 , pp. 2076
    • Maier, I.O.1    Sokolov, A.I.2
  • 19
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    • N. A. Shpot
    • N. A. Shpot;
  • 20
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    • The analytical expressions for the relevant three-loop Feynman integrals in (Formula presented) are listed in Ref. 19
    • Phys. Lett. A 142, 474 (1989). The analytical expressions for the relevant three-loop Feynman integrals in (Formula presented) are listed in Ref. 19.
    • (1989) Phys. Lett. A , vol.142 , pp. 474
  • 25
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    • The three-loop random bulk exponents (Formula presented) and (Formula presented) mentioned in the review part of this article were obtained in Ref. 18
    • R. Folk, Yu. Holovatch, and T. Yavors’kii, Phys. Rev. B 61, 15 114 (2000). The three-loop random bulk exponents (Formula presented) and (Formula presented) mentioned in the review part of this article were obtained in Ref. 18.
    • (2000) Phys. Rev. B , vol.61 , pp. 15 114
    • Folk, R.1    Holovatch, Y.2    Yavors’kii, T.3
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    • C. Domb and J. L. Lebowitz Academic Press, London
    • K. Binder, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1983), Vol. 8, pp. 1–144.
    • (1983) Phase Transitions and Critical Phenomena , vol.8 , pp. 1-144
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  • 42
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    • The original approach of Parisi 41 employing the massive field theory directly in fixed spatial dimensions (Formula presented) has been extended to the semi-infinite systems with surfaces in Refs. 42 43 35
    • The original approach of Parisi 41 employing the massive field theory directly in fixed spatial dimensions (Formula presented) has been extended to the semi-infinite systems with surfaces in Refs. 424335.
  • 55
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    • fact, this is an intuitive picture conveyed from the theory of bulk regular systems. Much less is known about the large-order behavior of perturbative expansions pertaining to infinite random systems (see Refs. 54 55 56), especially at large space dimensionalities. To our knowledge, there are no explicit results on large orders for surface quantities, even in the absence of disorder
    • In fact, this is an intuitive picture conveyed from the theory of bulk regular systems. Much less is known about the large-order behavior of perturbative expansions pertaining to infinite random systems (see Refs. 545556), especially at large space dimensionalities. To our knowledge, there are no explicit results on large orders for surface quantities, even in the absence of disorder.
  • 60
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    • A good example can be the correction-to-scaling exponent ω. A two-loop result at (Formula presented) is (Formula presented) 16. At the three-loop level, two different resummation schemes yield (Formula presented) and 0.376 18. These are in an excellent agreement with the recent result (Formula presented) of high-precision Monte Carlo calculations 26
    • A good example can be the correction-to-scaling exponent ω. A two-loop result at (Formula presented) is (Formula presented) 16. At the three-loop level, two different resummation schemes yield (Formula presented) and 0.376 18. These are in an excellent agreement with the recent result (Formula presented) of high-precision Monte Carlo calculations 26.


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