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
Uniqueness of Gibbs states for quantum lattice systems
Download PDF
Download PDF
  • Published: June 1997

Uniqueness of Gibbs states for quantum lattice systems

  • S. Albeverio1,
  • Y. G. Kondratiev2,
  • M. Röckner3 &
  • …
  • T. V. Tsikalenko2 

Probability Theory and Related Fields volume 108, pages 193–218 (1997)Cite this article

  • 100 Accesses

  • 25 Citations

  • Metrics details

Summary.

We prove uniqueness of Euclidean Gibbs states for certain quantum lattice systems with unbounded spins. We use Dobrushin’s uniqueness criterion. The necessary estimates for the Vasershtein distance between the corresponding one-point conditional distributions with boundary conditions differing only at one side, are obtained by proving a Log-Sobolev inequality on the infinite dimensional single spin (= loop) spaces. Some important classes of concrete examples to which all this applies are discussed.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Ruhr-Universität, D-44780 Bochum, Germany , , , , , , DE

    S. Albeverio

  2. BiBoS Research Centre, D-33615 Bielefeld, Germany , , , , , , DE

    Y. G. Kondratiev & T. V. Tsikalenko

  3. Fakultät für Mathematik, Bielefeld Universität, D-33615 Bielefeld, Germany, , , , , , DE

    M. Röckner

Authors
  1. S. Albeverio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. G. Kondratiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Röckner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. V. Tsikalenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 28 February 1996 / In revised form: 9 September 1996

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Albeverio, S., Kondratiev, Y., Röckner, M. et al. Uniqueness of Gibbs states for quantum lattice systems. Probab Theory Relat Fields 108, 193–218 (1997). https://doi.org/10.1007/s004400050107

Download citation

  • Issue Date: June 1997

  • DOI: https://doi.org/10.1007/s004400050107

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

  • Mathematics Subject Classification (1991): Primary: 60H30. Secondary: 31C25
  • 82B31
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