Communications in Mathematical Physics

, Volume 7, Issue 4, pp 337–348 | Cite as

Statistical mechanics of quantum spin systems. II

  • Derek W. Robinson
Article

Abstract

In the first part of this paper we continue the general analysis of quantum spin systems. It is demonstrated, for a large class of interactions, that time-translations form a group of automorphisms of theC*-algebra\(\mathfrak{A}\) of quasi-local observables and that the thermodynamic equilibrium states are invariant under this group. Further it is shown that the equilibrium states possess the Kubo-Martin-Schwinger analyticity and boundary condition properties. In the second part of the paper we give a general analysis of states which are invariant under space and time translations and also satisfy the KMS boundary condition. A discussion of these latter conditions and their connection with the decomposition of invariant states into ergodic states is given. Various properties pertinent to this discussion are derived.

Keywords

Boundary Condition Neural Network Statistical Physic Equilibrium State Complex System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Robinson, D. W.: Commun. Math. Phys.6 (1967).Google Scholar
  2. 2.
    Haag, R., N. Hugenholtz, andM. Winnink: Commun. Math. Phys.5, 215 (1967).Google Scholar
  3. 3.
    Reeh, H., andS. Schlieder: Nuovo Cimento22, 1051 (1961).Google Scholar
  4. 4.
    Kastler, D., andD. W. Robinson: Commun. Math. Phys.3, 151 (1966).Google Scholar
  5. 5.
    Ruelle, D.: Commun. Math. Phys.3, 133 (1966).Google Scholar
  6. 6.
    Araki, H.: Progr. Theoret. Phys. (Kyoto)32, 844 (1967).Google Scholar
  7. 7.
    Robinson, D. W., andD. Ruelle: Ann Inst. Henri Poincare VI, 299 (1967).Google Scholar
  8. 8.
    Glimm, J.: Trans. Am. Math. Soc.95, 318 (1960).Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Derek W. Robinson
    • 1
    • 2
  1. 1.Lyman Laboratory of PhysicsHarvard UniversityUSA
  2. 2.Theoretical Physics DivisionCERNGenfSchweiz

Personalised recommendations