Communications in Mathematical Physics

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

Correlation inequalities for Ising ferromagnets with symmetries

  • Gerhard C. Hegerfeldt


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.


Neural Network Statistical Physic Growth Condition Complex System Nonlinear Dynamics 
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  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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