Journal of Statistical Physics

, Volume 40, Issue 3–4, pp 563–575 | Cite as

Correlation inequalities for a class of even ferromagnets

  • Kei-ichi Kondo
  • Takeshi Otofuji
  • Yüki Sugiyama
Articles

Abstract

We present rigorous correlation inequalities for connectedn-point functions in a class of even ferromagnets. The class includes spin-1/2 Ising models and scalar field models with potential functionV which is even and continuously differentiable withV′ convex on [0, ∞). These inequalities are obtained by pushing ahead with the method of Ellis, Monroe, and Newman at its maximum.

Key words

Correlation inequality Ising model scalar field models 

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References

  1. 1.
    D. Ruelle,Statistical Mechanics: Rigorous Results (W. A. Benjamin, New York, 1969); J. Glimm and A. Jaffe,Quantum Physics: A Functional Integral Point of View (Springer, New York, 1981).Google Scholar
  2. 2.
    B. Simon,The P(φ) 2 Euclidean (Quantum) Field Theory (Princeton University Press, Princeton, 1974).Google Scholar
  3. 3.
    M. Aizenman,Phys. Rev. Lett. 47:1 (1981);Commun. Math. Phys. 86:1 (1982); J. Fröhlich,Nucl. Phys. B200[FS4]:281 (1982); C. Aragao de Carvalho, S. Caracciolo, and J. Fröhlich,Nucl. Phys. B215[FS7]:209 (1983); M. Aizenman and R. Graham,Nucl. Phys. B225[FS9]:209 (1983).Google Scholar
  4. 4.
    D. C. Brydges, J. Fröhlich, and A. D. Sokal,Commun. Math. Phys. 91:141 (1983).Google Scholar
  5. 5.
    R. S. Ellis and J. L. Monroe,Commun. Math. Phys. 41:33 (1975).Google Scholar
  6. 6.
    R. S. Ellis, J. L. Monroe, and C. M. Newman,Commun. Math. Phys. 46:167 (1976).Google Scholar
  7. 7.
    R. S. Ellis and Ch. M. Newman,Trans. Am. Math. Soc. 237:83 (1978).Google Scholar
  8. 8.
    G. S. Sylvester,J. Stat. Phys. 15:327 (1976).Google Scholar
  9. 9.
    B. Simon,Functional Integration and Quantum Physics (Academic Press, New York, 1979).Google Scholar
  10. 10.
    J. K. Percus,Commun. Math. Phys. 40:283 (1975).Google Scholar
  11. 11.
    G. S. Sylvester,Commun. Math. Phys. 42:209 (1975).Google Scholar
  12. 12.
    K.-I. Kondo, Nagoya Univ. preprint, DPNU-84-25.Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Kei-ichi Kondo
    • 1
  • Takeshi Otofuji
    • 1
  • Yüki Sugiyama
    • 1
  1. 1.Department of PhysicsNagoya UniversityNagoyaJapan

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