Advertisement

Journal of Statistical Physics

, Volume 30, Issue 2, pp 449–456 | Cite as

Self-avoiding walks with geometrical constraints

  • S. G. Whittington
Articles

Abstract

We consider self-avoiding walks on aD-dimensional hypercubic lattice, confined to a slab geometry and confined to a half-space. We present a proof of the existence of a “connective constant” for the slab geometry and review some corresponding results for the half-space. We also discuss the way in which scaling arguments can be used to give stronger, but nonrigorous, results.

Key words

Self-avoiding walks 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Hille,Functional Analysis and Semi-Groups, Am. Math. Soc. Colloq. Publ. No. 31 (American Mathematical Society, New York, 1948).Google Scholar
  2. 2.
    J. M. Hammersley and D. J. A. Welsh,Quart. J. Math. Oxford 13:108 (1962).Google Scholar
  3. 3.
    F. T. Wall, W. A. Seitz, J. C. Chin, and F. Mandel,J. Chem. Phys. 67:434 (1977).Google Scholar
  4. 4.
    F. T. Wall, J. C. Chin, and F. Mandel,J. Chem. Phys. 66:3066 (1977).Google Scholar
  5. 5.
    F. T. Wall and D. J. Klein,Proc. Nat. Acad. Sci. 76:1529 (1979).Google Scholar
  6. 6.
    M. Daoud and P. G. de Gennes,J. Phys. (Paris) 38:85 (1977).Google Scholar
  7. 7.
    A. J. Guttmann and S. G. Whittington,J. Phys. A 11:L107 (1978).Google Scholar
  8. 8.
    F. T. Wall, W. A. Seitz, J. C. Chin, and P. G. de Gennes,Proc. Nat. Acad. Sci. 75:2069 (1978).Google Scholar
  9. 9.
    B. Vincent and S. G. Whittington inSurface and Colloid Science, Vol. 12, E. Matijević, ed. (Plenum Press, New York, 1982).Google Scholar
  10. 10.
    S. G. Whittington,J. Chem. Phys. 63:779 (1975).Google Scholar
  11. 11.
    J. M. Hammersley,Proc. Camb. Phil. Soc. 57:516 (1961).Google Scholar
  12. 12.
    T. Ishinabe and S. G. Whittington,J. Phys. A 14:439 (1981).Google Scholar
  13. 13.
    A. Silberberg,J Chem. Phys. 46:1105 (1967).Google Scholar
  14. 14.
    M. N. Barber, A. J. Guttmann, K. M. Middlemiss, G. M. Torrie, and S. G. Whittington,J. Phys. A 11:1833 (1978).Google Scholar
  15. 15.
    K. M. Middlemiss and S. G. Whittington,J. Chem. Phys. 64:4684 (1976).Google Scholar
  16. 16.
    M. N. Barber,Phys. Rev. B 8:407 (1973).Google Scholar
  17. 17.
    J. M. Hammersley,Proc. Camb. Phil. Soc. 58:235 (1962).Google Scholar
  18. 18.
    J. B. Wilker and S. G. Whittington,J. Phys. A 12:L245 (1979).Google Scholar
  19. 19.
    A. J. Guttmann and S. G. Whittington,J. Phys. A 11:721 (1978).Google Scholar
  20. 20.
    D. A. Klarner,Can. J. Math. 19:851 (1967).Google Scholar
  21. 21.
    D. J. Klein,J. Chem. Phys. 75:5186 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • S. G. Whittington
    • 1
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada

Personalised recommendations