Skip to main content
SpringerLink
Log in

General properties of polymer systems

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We prove the existence of the thermodynamic limit for the pressure and show that the limit is a convex, continuous function of the chemical potential.

The existence and analyticity properties of the thermodynamic limit for the correlation functions is then derived; we discuss in particular the Mayer Series and the virial expansion.

In the special case of Monomer-Dimer systems it is established that no phase transition is possible; moreover it is shown that the Mayer Series for the density is a series of Stieltjes, which yields upper and lower bounds in terms of Padé approximants.

Finally it is shown that the results obtained for polymer systems can be used to study classical lattice systems.

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. Green, H. S., Leipnik, R.: Rev. Mod. Phys.32, 129 (1960).

    Google Scholar 

  2. Kasteleyn, P. W.: Physica27, 1209 (1961).

    Google Scholar 

  3. —— J. Math. Phys.4, 287 (1963); — Graph Theory and Theoretical Physics. New York: Academic Press 1967.

    Google Scholar 

  4. Levelt, J. M. H., Cohen, E. G. D.: Studies in Statistical Mechanics, Vol. II. Amsterdam: North Holland Publ. 1964.

    Google Scholar 

  5. Ruelle, D.: Statistical Mechanics, Section 2.4. New York: Benjamin 1969.

    Google Scholar 

  6. Heilmann, O. J., Lieb, E. H.: Phys. Rev. Letters24, 1412 (1970).

    Google Scholar 

  7. Ruelle, D.: (Ref. [3] ) Section 4.4.

    Google Scholar 

  8. —— (Ref. [3] ) Exercice 3D, p. 64.

    Google Scholar 

  9. —— (Ref. [3] ) Section 7.3.

    Google Scholar 

  10. Gallavotti, G., Miracle-Sole, S.: Commun. math. Phys.7, 274 (1968).

    Google Scholar 

  11. Ruelle, D.: (Ref. [3] ) Section 4.2.

    Google Scholar 

  12. Green, H. S., Hurst, C. A.: Order-Disorder Phenomena Monograph in Statistical Physics, Vol. 5. New York: Interscience 1964.

    Google Scholar 

  13. Kunz, H.: Phys. Letters32A, 311 (1970).

    Google Scholar 

  14. Baker, G., Gammel, J.: The Padé Approximant in Theoretical Physics, Theorem 10, p. 18–19. New York: Academic Press 1970.

    Google Scholar 

  15. —— —— The Padé Approximant in Theoretical Physics, Theorem 7, p. 11. New York: Academic Press 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique Théorique, Ecole Polytechnique Fédérale, Lausanne, Switzerland

    C. Gruber & H. Kunz

Authors
  1. C. Gruber
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Kunz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Work presented in partial fullfilment of the Ph. D. Thesis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gruber, C., Kunz, H. General properties of polymer systems. Commun.Math. Phys. 22, 133–161 (1971). https://doi.org/10.1007/BF01651334

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01651334

Keywords

Search

Navigation