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Communications in Mathematical Physics

, Volume 57, Issue 3, pp 259–266 | Cite as

Correlation inequalities for Ising ferromagnets with symmetries

  • Gerhard C. Hegerfeldt
Article

Abstract

We derive new correlation inequalities for even Ising ferromagnets whose interaction is invariant under some symmetry transformation and satisfies a growth condition. The recent results of Schrader [1] and Messager and Miracle-Sol [2] for the nearest neighbour (n.n.) Ising model reappear as a special case. In addition we obtain monotonicity of 〈σ0σ j 〉 under translation ofj perpendicular to diagonal hyperplanes and the inequality 〈σ0σ j 〉≧\(\left\langle {\sigma _0 \sigma _{\left( {\sum {\left| {j_\nu } \right|,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{0} } } \right)} } \right\rangle \) for n.n. and other interactions.

Keywords

Neural Network Statistical Physic Growth Condition Complex System Nonlinear Dynamics 
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.

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References

  1. 1.
    Schrader, R.: New correlation inequalities for the Ising model andP(φ) theories. Phys. Rev. B15, 2798 (1977)Google Scholar
  2. 2.
    Messager, A., Miracle-Sol, S.: Correlation functions and boundary conditions in the Ising ferromagnet. Preprint, Marseille 1977Google Scholar
  3. 3.
    Ginibre, J.: General formulation of Griffith's inequalities. Commun. math. Phys.16, 310 (1970)Google Scholar
  4. 4.
    Simon, B.: TheP(φ)2 Euclidean (quantum) field theory. Princeton: Princeton University Press 1974Google Scholar
  5. 5.
    McCoy, B.M., Wu, T.T.: The two-dimensional Ising model. Cambridge: Harvard University Press 1973Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Gerhard C. Hegerfeldt
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenFederal Republic of Germany

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