Abstract:
We prove that energy functions are positively correlated in isotropic, ferromagnetic O(N) models on an arbitrary graph. In our inductive proof, this is used to prove the strong FKG property of the Wolff representation for isotropic, ferromagnetic O(N+ 1) models. This strong FKG property is then used to prove energy correlations for the O(N+ 1) model. Furthermore, percolation in the Wolff representation is proved to be a necessary and sufficient condition for positivity of the spontaneous magnetization (previously known only for N= 3).
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Received: 7 March 2000 / Accepted: 31 October 2000
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Campbell, M. Energy Correlations in O(N) Models¶and the Wolff Representation. Commun. Math. Phys. 218, 99–111 (2001). https://doi.org/10.1007/s002200100380
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DOI: https://doi.org/10.1007/s002200100380