Skip to main content
SpringerLink
Log in

Exactly solvable lattice model of rooted branched polymers

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

A lattice model of rooted branched polymers that has an exact solution in all dimensions is considered. Kirchhoff's theorem is used to calculate the partition function of the model. Universal behavior of the thermodynamic functions of the model in the close-packing limit is found. A matrix procedure for calculating the correlation functions is developed. The mean number of atoms of a polymer with given valence is calculated for arbitrary densities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. H. Fowler and G. S. Rushbrooke,Trans. Faraday Soc.,33, 1272 (1937).

    Google Scholar 

  2. H. N. V. Temperley, and M. E. Fisher,Philos. Mag.,6, 1061 (1961).

    Google Scholar 

  3. P. W. Kasteleyn,Physica (Utrecht),27, 1209 (1961).

    Google Scholar 

  4. S. R. Broadbent and J. M. Hammersley,Proc. Cambridge Philos. Soc.,53, 629 (1957).

    Google Scholar 

  5. F. Harary,Graph Theory, Addison-Wesley, Reading, Mass. (1969).

    Google Scholar 

  6. T. C. Lubensky and J. Isaacson,Phys. Rev. A,20, 2130 (1979).

    Google Scholar 

  7. E. I. Kornilov and V. B. Priezzhev,Phys. Lett. A,102, 32 (1984).

    Google Scholar 

  8. E. I. Kornilov and V. B. Priezzhev, Preprint R17-86-168 [in Russian], JINR, Dubna (1986).

  9. D. J. Klein,J. Chem. Phys.,75, 5186 (1981).

    Google Scholar 

  10. V. B. Priezzhev,Teor. Mat. Fiz.,31, 89 (1977).

    Google Scholar 

  11. J. L. Cardy, in:Phase Transitions and Critical Phenomena (eds. C. Domb and J. L. Lebowitz), Vol. 11 (1987), p. 55.

  12. V. Privman,Phys. Rev. B,38, 9261 (1988).

    Google Scholar 

  13. B. Duplantier and F. David,J. Stat. Phys.,51, 327 (1988).

    Google Scholar 

  14. J. G. Brankov and V. B. Priezzhev,J. Phys. A,25, 4297 (1992).

    Google Scholar 

  15. P. Bak, C. Tang, and K. Wiesenfeld,Phys. Rev. A,38, 364 (1988).

    Google Scholar 

  16. D. Dhar,Phys. Rev. Lett.,64, 1613 (1990).

    Google Scholar 

  17. V. B. Priezzhev, Preprint DIAS (1992).

  18. C. Kirchhoff,Ann. Phys. Chem.,72, 497 (1847).

    Google Scholar 

  19. H. N. V. Temperley,Faraday Soc. Discuss.,25, 92 (1958).

    Google Scholar 

  20. J. W. Essam and M. E. Fisher,Rev. Mod. Phys.,42, 272 (1970).

    Google Scholar 

  21. C. M. Fortuin and P. W. Kasteleyn,Physica (Utrecht),57, 536 (1972).

    Google Scholar 

  22. B. N. Shklovskii and A. L. Éfros,Usp. Fiz. Nauk,117, 425 (1975).

    Google Scholar 

  23. M. Hall,Combinatorial Theory, Waltham, Mass. (1967).

  24. V. B. Priezzhev,Usp. Fiz. Nauk,147, 747 (1985).

    Google Scholar 

  25. E. I. Kornilov and V. B. Priezzhev,Z. Phys. B,54, 351 (1984).

    Google Scholar 

  26. E. W. Montroll,J. Sci. Ind. Appl. Math.,4, 241 (1956).

    Google Scholar 

  27. D. S. Gaunt,Phys. Rev.,179, 174 (1969).

    Google Scholar 

  28. E. W. Montroll and B. J. West,Fluctuation Phenomena (eds. E. W. Montroll and J. L. Lebowitz), North-Holland, Amsterdam (1979), Chap. 2, p. 61.

    Google Scholar 

  29. F. Y. Wu,Phys. Rev. B,18, 515 (1978).

    Google Scholar 

  30. J. P. Straley,Phys. Rev. B,19, 4855 (1979).

    Google Scholar 

  31. W. D. Braswell, F. Family, and J. P. Straley,Phys. Rev. A,29, 254 (1984).

    Google Scholar 

  32. E. W. Montroll,Stability and Phase Transitions [Russian translation], Mir, Moscow (1973).

    Google Scholar 

  33. A. Seitz and D. J. Klein,J. Chem. Phys.,75, 5190 (1981).

    Google Scholar 

  34. D. Dhar and S. S. Manna, submitted toPhys. Rev. B (1992).

Download references

Authors
  1. E. I. Kornilov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. B. Priezzhev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Joint Institute for Nuclear Research, Dubna. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 90–105, January, 1994.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kornilov, E.I., Priezzhev, V.B. Exactly solvable lattice model of rooted branched polymers. Theor Math Phys 98, 61–71 (1994). https://doi.org/10.1007/BF01015125

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01015125

Keywords

Search

Navigation