Finite-Size Scaling Theory

  • V. Rittenberg
Part of the NATO Advanced Study Institutes Series book series (volume 82)

Abstract

Fisher’s1 finite-size scaling describes the cross-over from the singular behaviour of thermodynamic quantities at the critical point to the analytic behaviour of a finite system. In the last two years the method was extended to the transfer matrix technique by Nightingale and Blöte2 and to the Hamiltonian formalism3 by Hamer and Barber4–6. We will be concerned only with these applications.

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References

  1. 1.
    M.E. Fisher, Critical Phenomena, in Proc. Enrico Fermi Intern. School of Physics, M.S. Green ed. (Academic Press, N.Y. 1971)Google Scholar
  2. 2.
    M.P. Nightingale and H.W.J. Blote, Physica 104A, 352 (1980)CrossRefGoogle Scholar
  3. H.W.J. Blöte, M.P. Nightingale and B. Derrida, J. Phys. A14, L45 (1981)ADSGoogle Scholar
  4. 3.
    J. Kogut, Rev. Mod. Phys. 51, 689 (1979)MathSciNetADSCrossRefGoogle Scholar
  5. 4.
    C.J. Hamer and M.N. Barber, J. Phys. A13, L169 (1980)Google Scholar
  6. C.J. Hamer and M.N. Barber, J. Phys. 14, 241 (1981)MathSciNetADSGoogle Scholar
  7. 5.
    C.J. Hamer and M.N. Barber, J. Phys. A14, 259 (1981)MathSciNetADSGoogle Scholar
  8. 5.
    C.J. Hamer and M.N. Barber, J. Phys. A14, 2009 (1981)ADSGoogle Scholar
  9. M.N. Barber and P.M. Duxbury, J. Phys. A14. L251 (1981)MathSciNetADSGoogle Scholar
  10. 6.
    H.H. Roomany, H.W. Wyld and L.E. Holloway, Phys. Rev. D21, 1557 (1980)MathSciNetADSGoogle Scholar
  11. H.H. Roomany and H.W. Wyld, Phys. Rev. D21, 3341 (1980), Phys. Rev. B23, 1357 (1981)MathSciNetADSGoogle Scholar
  12. 7.
    P. Centen, V. Rittenberg and M. Marcu, Preprint Bonn-HE-81–29Google Scholar
  13. 8.
    J.M. Vanden Broeck and L.W. Schwartz, SIAM J. Math. Anal. 10, 658 (1979)MathSciNetMATHCrossRefGoogle Scholar
  14. 9.
    R.J. Baxter, Ann. Phys. (N.Y.) 70, 193 (1972)MathSciNetADSMATHCrossRefGoogle Scholar
  15. 10.
    J. Ashkin and E. Teller, Phys. Rev. 64, 178 (1942)ADSCrossRefGoogle Scholar
  16. 11.
    M. N. Barber, J. Phys. A12, 679 (1979)ADSGoogle Scholar
  17. 12.
    Th. Niemeyer, Physica 36, 377 (1967)ADSCrossRefGoogle Scholar
  18. 13.
    S. Elizur, R. B. Pearson and J. Shigemitsu, Phys. Rev. D19, 3698 (1979)ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • V. Rittenberg
    • 1
  1. 1.Physikalisches InstitutBonn UniversityGermany

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