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Volumn 68, Issue 22, 2003, Pages

Relevance of space anisotropy in the critical behavior of m-axial Lifshitz points

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; ARTICLE; CALCULATION; FOURIER TRANSFORMATION; MAGNETIC FIELD; MATHEMATICAL ANALYSIS; MATHEMATICAL PARAMETERS; MODEL; SPACE; THERMODYNAMICS;

EID: 0742280370     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.68.224415     Document Type: Article
Times cited : (16)

References (32)
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    • F. J. W. Hahne, Vol. 186 of Lecture Notes in PhysicsSpringer-Verlag, Berlin
    • M. E. Fisher, in Critical Phenomena, edited by F. J. W. Hahne, Vol. 186 of Lecture Notes in Physics (Springer-Verlag, Berlin, 1983), pp. 1–139.
    • (1983) Critical Phenomena , pp. 1-139
    • Fisher, M.E.1
  • 3
    • 0001348177 scopus 로고
    • C. Domb and J. L. LebowitzAcademic, London
    • A. Aharony, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1976), Vol. 6, pp. 358–424.
    • (1976) Phase Transitions and Critical Phenomena , vol.6 , pp. 358-424
    • Aharony, A.1
  • 4
    • 0003242030 scopus 로고
    • C. Domb and J. L. LebowitzAcademic, London
    • W. Selke, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1992), Vol. 15, pp. 1–72.
    • (1992) Phase Transitions and Critical Phenomena , vol.15 , pp. 1-72
    • Selke, W.1
  • 7
    • 85038993961 scopus 로고    scopus 로고
    • For background and extensive lists of references, see the review articles in Refs. 8 and 9
    • For background and extensive lists of references, see the review articles in Refs. 8 and 9.
  • 9
    • 0036025979 scopus 로고    scopus 로고
    • Proceedings of the 5th International Conference “Renormalization Group 2002,” Tatranska Strba, High Tatra Mountains, Slovakia, March 2002
    • H.W. Diehl, Acta Phys. Slov. 52, 271 (2002), Proceedings of the 5th International Conference “Renormalization Group 2002,” Tatranska Strba, High Tatra Mountains, Slovakia, March 2002.
    • (2002) Acta Phys. Slov. , vol.52 , pp. 271
    • Diehl, H.W.1
  • 23
    • 4143059761 scopus 로고
    • 5th ed., Vol. VII of Lehrbuch der Theoretischen PhysikAkademie Verlag, Berlin
    • L. D. Landau and E. M. Lifschitz, Elastizitätstheorie, 5th ed., Vol. VII of Lehrbuch der Theoretischen Physik (Akademie Verlag, Berlin, 1983).
    • (1983) Elastizitätstheorie
    • Landau, L.D.1    Lifschitz, E.M.2
  • 24
    • 85039005246 scopus 로고    scopus 로고
    • There are fewer tensors (Formula presented) than elastic moduli (Formula presented) because the latter are not totally symmetric but satisfy in general only the relations (Ref. 23) (Formula presented)
    • There are fewer tensors (Formula presented) than elastic moduli (Formula presented) because the latter are not totally symmetric but satisfy in general only the relations (Ref. 23) (Formula presented).
  • 25
    • 85039008486 scopus 로고    scopus 로고
    • To investigate the Lifshitz-point critical behavior in the spherical limit (Formula presented), Frachebourg and Henkel (Ref. 26) considered a Hamiltonian of the form (10) but without the isotropic derivative term (Formula presented). In RG analyses such a simplifying assumption cannot be maintained because this term gets generated under the RG, even within the framework of the 1/n expansion
    • To investigate the Lifshitz-point critical behavior in the spherical limit (Formula presented), Frachebourg and Henkel (Ref. 26) considered a Hamiltonian of the form (10) but without the isotropic derivative term (Formula presented). In RG analyses such a simplifying assumption cannot be maintained because this term gets generated under the RG, even within the framework of the 1/n expansion.
  • 29
    • 85038989419 scopus 로고    scopus 로고
    • MATHEMATICA, version 3.0, a product of Wolfram Research
    • MATHEMATICA, version 3.0, a product of Wolfram Research.
  • 30
    • 85038992948 scopus 로고    scopus 로고
    • We have verified that our numerical integration method gives values for m = 2 and m = 6 in conformity with the analytical results (52). Yet, in the m = 6 case, we have contented ourselves with a numerical accuracy ≲0.4%. The additional decimals given in Table I were determined from the exact expression (52). For m = 2, the numerical accuracy is higher, corresponding essentially to the number of decimals given
    • We have verified that our numerical integration method gives values for m = 2 and m = 6 in conformity with the analytical results (52). Yet, in the m = 6 case, we have contented ourselves with a numerical accuracy ≲0.4%. The additional decimals given in Table I were determined from the exact expression (52). For m = 2, the numerical accuracy is higher, corresponding essentially to the number of decimals given.
  • 31
    • 0000585079 scopus 로고
    • The sole exception, to our knowledge, is
    • The sole exception, to our knowledge, is D. Mukamel and M. Luban, Phys. Rev. B 18, 3631 (1978).
    • (1978) Phys. Rev. B , vol.18 , pp. 3631
    • Mukamel, D.1    Luban, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.