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Susceptibility of the rectangular Ising ferromagnet

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Abstract

The critical index valuesγ= 7/4 for the susceptibility andδ=15 for the critical isotherm are derived rigorously for the rectangular Ising ferromagnet with nearest neighbor interactions. The critical indices associated with the Fisher moment definition of the correlation length are obtained asT→T c+. The index of the fluctuation sum definition of critical correlations is obtained.

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References

  1. D. B. Abraham,Comm. Math. Phys. 59:17 (1978);60:181 (1978).

    Google Scholar 

  2. D. B. Abraham and P. Reed,Phys. Rev. Lett. 33:377 (1974);Comm. Math. Phys. 49:35 (1976).

    Google Scholar 

  3. D. B. Abraham,Phys. Lett. 39A:375 (1972).

    Google Scholar 

  4. E. Barouch, B. M. McCoy, and T. T. Wu,Phys. Rev. Lett. 31:1409 (1973); C. A. Tracy and B. M. McCoy,Phys. Rev. Lett. 31:1500 (1973); T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch,Phys. Rev. B 13:316 (1976).

    Google Scholar 

  5. D. B. Abraham,Phys. Lett. 43A:163 (1973).

    Google Scholar 

  6. G. Gallavotti,Riv. Nuovo Cimento 2:133 (1972).

    Google Scholar 

  7. J. L. Lebowitz,Comm. Math. Phys. 28:313 (1972).

    Google Scholar 

  8. D. B. Abraham and H. Kunz,Phys. Rev. Lett. 39:1011 (1977).

    Google Scholar 

  9. M. E. Fisher,Physica 25:521 (1959);28:172 (1962).

    Google Scholar 

  10. L. P. Kadanoff,Nuovo Cimento 44B:276 (1966).

    Google Scholar 

  11. L. Onsager,Phys. Rev. 65:117 (1944).

    Google Scholar 

  12. A. Messager and S. Miracle-Sole,J. Stat. Phys. 17:245 (1978).

    Google Scholar 

  13. B. M. McCoy and T. T. Wu,The Two-Dimensional Ising Ferromagnet (Harvard University Press, 1973).

  14. M. E. Fisher and R. J. Burford,Phys. Rev. 156:583 (1967).

    Google Scholar 

  15. R. B. Griffiths,J. Math. Phys. 8:478, 484 (1967).

    Google Scholar 

  16. R. B. Griffiths,J. Chem. Phys. 43:1958 (1965).

    Google Scholar 

  17. L. Onsager,Nuovo Cimento (Suppl.) 6:261 (1949); C. N. Yang,Phys. Rev. 85:808 (1952); G. Bennettin, G. Gallavotti, G. Jona-Lasinio, and A. L. Stella,Comm. Math. Phys. 30:45 (1973); D. B. Abraham and A. Martin-Lof,Comm. Math. Phys. 32:245 (1973).

    Google Scholar 

  18. D. S. Gaunt and M. F. Sykes,Solid State Phys. 5C:1429 (1972).

    Google Scholar 

  19. E. R. Caianiello,Combinatorics and Renormalisation in Quantum Field Theory (W. A. Benjamin, 1973).

  20. G. V. Ryazonov,Zh. Eksp. Teor. Fiz. 49:1134 (1965).

    Google Scholar 

  21. V. G. Vaks, A. I. Larkin, and Yu. N. Ovchinnikov,Zh. Eksp. Teor. Fiz. 49:1180 (1965) [Sov. Phys.-JETP 22:820 (1966)].

    Google Scholar 

  22. M. E. Fisher,Phys. Rev. 180:594 (1969).

    Google Scholar 

  23. J. D. Johnson, S. Krinsky, and B. McCoy,Phys. Rev. A 8:2526 (1973).

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical Chemistry, University of Oxford, Oxford, England

    D. B. Abraham

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  1. D. B. Abraham
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Partially supported by grant PHY 76 17191.

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Abraham, D.B. Susceptibility of the rectangular Ising ferromagnet. J Stat Phys 19, 349–358 (1978). https://doi.org/10.1007/BF01011754

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