Abstract
We establish a variety of results using the Holsztynski-Slawny reduction method to study various ferromagnetic, Ising spin systems. The results range from a new proof of the lack of a first-order phase transition for certain infinite range, pair interaction, one-dimensional systems to a study of certain three-dimensional systems having many-body interactions.
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References
J. Slawny,Commun. Math. Phys. 46:75 (1976).
W. Holsztynski and J. Slawny,Lett. Nuovo Cimento 13:534 (1975).
W. Holsztynski and J. Slawny,Commun. Math. Phys. 66:147 (1979).
J. Slawny, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, 1986).
J. A. Barker,Phys. Rev. Lett. 57:230 (1986).
H.-Y. Kim and M. W. Cole,Phys. Rev. B 35:3990 (1987).
M. Kolb and K. A. Penson,J. Phys. A: Math. Gen. 19:L779 (1986).
J. L. Monroe,J. Phys. A: Math. Gen. 19:2499 (1982).
J. Slawny, private communication.
D. C. Mattis and R. Galler,Phys. Rev. B 27:2894 (1983).
T. Horiguchi and T. Morita,Phys. Lett. 105a:57 (1984).
H. P. Griffiths and D. W. Wood,J. Phys. C: Solid State Phys. 6:2533 (1974).
F. J. Dyson,Commun. Math. Phys. 12:91 (1969).
D. Ruelle,Commun. Math. Phys. 9:267 (1968).
J. L. Lebowitz,J. Stat. Phys. 16:3 (1977).
A. Martin-Lof,Commun. Math. Phys. 24:253 (1972).
M. Suzuki,Phys. Rev. Lett. 28:507 (1972).
J. M. Debierre and L. Turban,J. Phys. A: Math. Gen. 16:3571 (1983).
H. W. J. Blote, A. Compagner, P. A. M. Cornelissen, A. Hoogtand, F. Mallezie, and C. Vanderzande,Physica 139A:395 (1986).
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Monroe, J.L. Results from the Holsztynski-Slawny reduction method for ferromagnetic Ising models. J Stat Phys 51, 195–203 (1988). https://doi.org/10.1007/BF01015326
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DOI: https://doi.org/10.1007/BF01015326