Abstract
Using the GKS inequality Griffiths and Kaufman showed in [12] that the susceptibility in the Ising model on the hierarchical lattices is infinite forT>T c . In the present work we give an analytic calculation of the dominant singularity of the susceptibility whenh→0 forT>T c . Moreover we analytically find the spontaneous magnetization forT<T c and prove that forT<T c the susceptibility is finite.
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Communicated by Ya. G. Sinai
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Bleher, P.M., Žalys, E. Asymptotics of the susceptibility for the Ising model on the hierarchical lattices. Commun.Math. Phys. 120, 409–436 (1989). https://doi.org/10.1007/BF01225505
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DOI: https://doi.org/10.1007/BF01225505