Geodesic
Spherical limit of $n$-vector correlations
Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 3, pp. 460-471

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It is shown that for any summable translationally invariant interaction the correlation functions of any order of the classical Heisenberg model ($n$-vector model) as $n\to\infty$ and for any fixed constant temperature $T$ converge to the corresponding correlation functions of the Berlin–Kac spherical model. A simple proof of the equality of the free energies of these models in the limit $n\to\infty$ is obtained in the process. The form that the result will take in the case without translational invariance is indicated. 
@article{TMF_1988_77_3_a12,
     author = {M. V. Shcherbina},
     title = {Spherical limit of $n$-vector correlations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {460--471},
     publisher = {mathdoc},
     volume = {77},
     number = {3},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_77_3_a12/}
}
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M. V. Shcherbina. Spherical limit of $n$-vector correlations. Teoretičeskaâ i matematičeskaâ fizika, Tome 77 (1988) no. 3, pp. 460-471. http://geodesic.mathdoc.fr/item/TMF_1988_77_3_a12/