Advertisement

Interpolation Between Dimensions

  • M. A. Novotny
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 74)

Abstract

A method is presented which allows one to interpolate between integer dimensions in a translationally invariant fashion using finite size transfer matrices. For the ferromagnetic Ising model an exact solution is presented for interpolation between isolated spins and d = 1, and finite strip calculations are presented for interpolation between d= 1 and d= 2. A possible application of this interpolation scheme is the numerical study of quantum spin systems.

Keywords

Partition Function Ising Model Transfer Matrix Quantum Spin System Finite Strip 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28 240 (1972).ADSCrossRefGoogle Scholar
  2. [2]
    D. J. Wallace and R. K. P. Zia, Phys. Rev. Lett. 43 808 (1979); D. Forster and A. Gabriunas, Phys. Rev. A 23 2627 (1981).CrossRefGoogle Scholar
  3. [3]
    R. Abe, Prog. Theor. Phys. (Kyoto) 47 62 (1972).ADSCrossRefGoogle Scholar
  4. [4]
    G. A. Baker, Jr. and L. P. Benofy, J. Stat. Phys. 29 699 (1982).MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    Y. Gefen, A. Aharony, Y. Shapir, and B. B. Mandelbrot, J. Phys. A 17 435 (1984).MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    M. A. Novotny, J. Math. Phys. 20 1146, 1979.MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971 ).Google Scholar
  8. [8]
    K. Huang, Statistical Mechanics (John Wiley & Sons, Inc., New York, 1963 ).Google Scholar
  9. [9]
    L. Onsager, Phys. Rev. 65 117 (1944).MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. [10]
    H. A. Kramers and G. H. Wannier, Phys. Rev. 60 252 (1941).MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. [11]
    M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities (Allyn and Bacon, Inc., Boston, 1964 ).zbMATHGoogle Scholar
  12. [12]
    H. Gutfreund and W. A. Little, Am. J. Phys. 50 219 (1982).ADSCrossRefGoogle Scholar
  13. [13]
    V. Privman and M. E. Fisher, J. Stat. Phys. 33 385 (1983).MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    R. B. Griffiths and P. D. Gujrati, J. Stat. Phys. 30 563 (1983).MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    H. F. Trotter, Proc. Am. Math. Soc. 10 545 (1959);Google Scholar
  16. M. Suzuki, Commun. Math. Phys. 51 183 (1976), 57 193 (1977).ADSzbMATHCrossRefGoogle Scholar
  17. [16]
    M. Suzuki, J. Stat. Phys. 43 883 (1986), and references therein.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • M. A. Novotny
    • 1
  1. 1.IBM Bergen Scientific CenterBergenNorway

Personalised recommendations