Scaling of Confined 4He at the Superfluid Transition

  • Francis M. Gasparini
  • Ilsu Rhee
Part of the NATO ASI Series book series (NSSB, volume 257)


4He at the superfluid transition has been well studied and has yielded valuable checks on aspects of critical behavior ranging from scaling, universality and explicit predictions of critical exponents and amplitude ratios. The most detailed results have been obtained in the thermodynamic limit, i.e., in situations where the smallest confining dimension for the helium sample is much larger than the magnitude of the critical correlation length, ξ. Since this length diverges at the transition, there are many experimental realizations, such as helium films or helium confined in pores, where the effect of confinement to dimensions comparable to ξ manifests itself as a modification of the properties realized in the thermodynamic limit, or as completely new behavior associated with a lower spacial dimension.


Correlation Length Scaling Function Bulk Behavior Superfluid Density Superfluid Transition 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M.E. Fisher, in “Critical Phenomena”, Proceedings of the 51st Enrico Fermi Summer School, Varenna, Italy, M.S. Green, ed., Academic Press, New York (1971).Google Scholar
  2. 2.
    M.N. Barber, in “Phase Transitions and Critical Phenomena”, Vol. 8, C. Domb and J.L. Lebowitz, eds., Academic Press, London, p. 145 (1983).Google Scholar
  3. 3.
    V. Privman, “Finite Size Scaling and Numerical Simulation of Statistical Systems,” V. Privman, ed., World Scientific, Singapore (1990).Google Scholar
  4. 4.
    T.-P. Chen and F.M. Gasparini, Phys. Rev. Lett. 40, 331 (1978).ADSCrossRefGoogle Scholar
  5. 5.
    F.M. Gasparini, T.-P. Chen and B. Bhattacharyya, Phys. Rev. B23, 5797 (1981).CrossRefGoogle Scholar
  6. 6.
    F.M. Gasparini, G. Agnolet and J.D. Reppy, Phys. Rev. B29, 138 (1984).ADSCrossRefGoogle Scholar
  7. 7.
    I. Rhee, F.M. Gasparini, and D.J. Bishop, Phys. Rev. Lett. 63, 410 (1989).ADSCrossRefGoogle Scholar
  8. 8.
    F.M. Gasparini and I. Rhee, to appear in “Progress in Low Temperature Physics,” vol. XIII, D.F. Brewer, ed., North-Holland, Amsterdam.Google Scholar
  9. 9.
    I. Rhee, D.J. Bishop, A. Petrou and F.M. Gasparini, Rev. Sci. Inst. 61, 1528 (1990).ADSCrossRefGoogle Scholar
  10. 10.
    J.S. Brooks, B.B. Sabo, P.C. Schubert and W. Zimmermann, Jr., Phys. Rev. B9, 4524 (1979).ADSCrossRefGoogle Scholar
  11. 11.
    P.C. Schubert and W. Zimmermann, Jr., J. Low Temp. Phys. 44, 177 (1981).Google Scholar
  12. 12.
    R.P. Henkel, E.N. Smith and J.D. Reppy, Phys. Rev. Lett. 23, 1276 (1969).ADSCrossRefGoogle Scholar
  13. 13.
    E.N. Smith, Ph.D. thesis, Cornell University, unpublished (1971).Google Scholar
  14. 14.
    D.F. McQueeney, Ph.D. theses, Cornell University, unpublished (1988).Google Scholar
  15. 15.
    W. Huhn and V. Dohm, Phys. Rev. Lett. 61, 1368 (1988).ADSCrossRefGoogle Scholar
  16. 16.
    R. Schmolke, A. Wacker, V. Dohm and D. Frank, LT-19 (1990).Google Scholar
  17. 17.
    E.S. Sabisky and C.H. Anderson, Phys. Rev. Lett. 30, 1122 (1973).ADSCrossRefGoogle Scholar
  18. 18.
    J. Maps and R.B. Hallock, Phys. Rev. Lett. 47, 1533 (1981).ADSCrossRefGoogle Scholar
  19. 19.
    Y.Y. Yu, D. Finotello and F.M. Gasparini, Phys. Rev. B 39, 6519 (1989).ADSCrossRefGoogle Scholar
  20. 20.
    X.F. Wang, I. Rhee and F.M. Gasparini, LT-19 (1990).Google Scholar
  21. 21.
    D. Finotello, Y.Y. Yu, X.F. Wang and F.M. Gasparini, LT-19 (1990).Google Scholar
  22. 22.
    V. Privman, preprint (1990).Google Scholar
  23. 23.
    I Rhee, D.J. Bishop and F.M. Gasparini, LT-19 (1990).Google Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • Francis M. Gasparini
    • 1
  • Ilsu Rhee
    • 1
  1. 1.Department of Physics and AstronomyState University of New York at BuffaloBuffaloUSA

Personalised recommendations