Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Completely analytic interactions with infinite values
Download PDF
Download PDF
  • Published: September 1990

Completely analytic interactions with infinite values

  • R. L. Dobrushin1 &
  • V. Warstat2 

Probability Theory and Related Fields volume 84, pages 335–359 (1990)Cite this article

  • 93 Accesses

  • 6 Citations

  • Metrics details

Summary

In this note we extend the notion of completely analytic interactions of Gibbs random fields that is known for finite interactions with finite range to interactions that can have infinite values, too. We formulate a set of ten conditions on such interactions in terms of analyticity properties of the partition functions, or correlation decay. The main theorem states that all these conditions are equivalent. Therefore, an interaction is called a completely analytic interaction, if it satisfies one of these conditions.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Dobrushin, R.L.: The uniqueness problem for Gibbs random fields and the problem of phase transitions (russ.). Funkts. Anal. Prilozh.2, 44–57 (1968)

    Google Scholar 

  2. Dobrushin, R.L.: The description of systems of random variables by the help of conditional probabilities (russ.). Teor. Verojatn. Primen.15, 469–497 (1970)

    Google Scholar 

  3. Dobrushin, R.L., Kolafa, J., Shlosman, S.B.: Phase diagram of the two-dim. Ising antiferromagnet (Computer assisted proof). Commun. Math. Phys.102, 89–103 (1985)

    Google Scholar 

  4. Dobrushin, R.L., Martirosyan, M.R.: Nonfinite perturbations of Gibbs fields (russ.). Teor. Mat. Fiz.74, 16–28 (1988)

    Google Scholar 

  5. Dobrushin, R.L., Shlosman, S.B.: Completely analytical Gibbs fields (russ.). Preprint, Moscow, 1986

  6. Dobrushin, R.L., Shlosman, S.B.: Completely analytical interactions: Constructive description. J. Stat. Phys.46, 983–1014 (1987)

    Google Scholar 

  7. Dobrushin, R.L., Shlosman, S.B.: Completely analytical Gibbs fields. In: Statistical physics and dynamical systems. Boston Basel Stuttgart: Birkhäuser, 1986

    Google Scholar 

  8. Malyshev, V.A., Minlos, R.A.: Gibbs random fields (russ.). Nauka, Moscow, 1985

    Google Scholar 

  9. Racz, Z.: Phase boundary of Ising antiferromagnets nearH=H c andT=0: Results from hard core lattice gas calculations. Phys. Rev.,B21, 4012–4016 (1980)

    Google Scholar 

  10. Ruelle, D.: Thermodynamic formalism. London Amsterdam: Addison-Wesley Publ. Comp., Tokyo: Don Mills, 1978

    Google Scholar 

  11. Ruelle, D.: Statistical mechanics: Rigorous results. New York Amsterdam: W.A. Benjamin Inc., 1969

    Google Scholar 

  12. Warstat, V.: A uniqueness theorem for systems of interacting polymers. Commun. Math. Phys.102, 47–58 (1985)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Information Transmission Problems of the Academy of Sciences, ul. Ermolovoi 19, 103051, Moscow K-51, USSR

    R. L. Dobrushin

  2. Sektion Mathematik, Martin-Luther-Universität Halle-Wittenberg, Postfach, DDR-4010, Halle, a.d. Saale, German Democratic Republic

    V. Warstat

Authors
  1. R. L. Dobrushin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Warstat
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dobrushin, R.L., Warstat, V. Completely analytic interactions with infinite values. Probab. Th. Rel. Fields 84, 335–359 (1990). https://doi.org/10.1007/BF01197889

Download citation

  • Received: 28 March 1988

  • Revised: 26 May 1989

  • Issue Date: September 1990

  • DOI: https://doi.org/10.1007/BF01197889

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Stochastic Process
  • Partition Function
  • Probability Theory
  • Random Field
  • Mathematical Biology
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature