Abstract
We generalize a theorem of Holley to include the case of continuous spins. Holley's theorem is itself a generalization of the inequalities due to Fortuin, Kastelyn and Ginibre.
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Birkhoff, G.: Lattice Theory. Am. Math. Soc., Providence, R.I. (1967)
Fortuin, C. M., Kasteleyn, P. W., Ginibre, J.: Commun. math. Phys.22, 89–103 (1971)
Holley, R.: Remarks on the FKG inequalities. Commun. math. Phys.36, 227–231 (1974)
Holley, R.: This proof can be found in an unpublished senior thesis directed by R. Holley, at Princeton's University
Several people working in classical and quantum statistical mechanics have noticed that this can be done, see for example Guerra, Rosen and Simon “The P(φ)2 Euclidean quantum field theory as classical statistical mechanics”. To appear
Cartier, P.: Seminiaire Bourbaki, No. 431, 1972/73
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Communicated by G. Gallavotti
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Preston, C.J. A generalization of the FKG inequalities. Commun.Math. Phys. 36, 233–241 (1974). https://doi.org/10.1007/BF01645981
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DOI: https://doi.org/10.1007/BF01645981