Abstract
The partition function for ferromagnetic plane rotators in a complex external field μ, with ¦Im μ¦ ⩽ ¦Re μ ¦, is bounded below in modulus by its value at μ=0. The proof is based on complex combinations of duplicated variables which are positive definite on a subgroup of the configuration group. In the isotropic situation (and μ=0), the associated “Gaussian inequalities” imply that all truncated correlation functions decay at least as the two-point function.
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References
T. Asano,Progr. Theor. Phys. 40:1328 (1968);J. Phys. Soc. Japan 25:1220 (1968).
J. Bricmont,J. Stat. Phys. 17:289 (1977).
F. Dunlop,J. Stat. Phys. 17:215 (1977).
F. Dunlop,Commun. Math. Phys. 49:247 (1976).
F. Dunlop and C. M. Newman,Commun. Math. Phys. 44:223 (1975).
J. Feldman,Can. J. Phys. 52:1583 (1974).
J. Fröhlich, inLes méthodes mathématiques de la théorie quantique des champs (CNRS, Paris, 1976).
J. L. Lebowitz,Commun. Math. Phys. 35:87 (1974).
T. D. Lee and C. N. Yang,Phys. Rev. 87:410 (1952).
C. M. Newman,Z. Wahrscheinlichkeitstheorie 33:15 (1975/76); Commun.Math.Phys.41:1 (1975).
T. Spencer,Commun. Math. Phys. 39:77 (1974).
M. Suzuki and M. E. Fisher,J. Math. Phys. 12:235 (1971).
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Dunlop, F. Zeros of the partition function and Gaussian inequalities for the plane rotator model. J Stat Phys 21, 561–572 (1979). https://doi.org/10.1007/BF01011168
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DOI: https://doi.org/10.1007/BF01011168