Journal de Physique I

Sommaire

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DOI: 10.1051/jp1:1996156
J. Phys. I France 6 (1996) 1435-1450

Magnetization and Overlap Distributions of the Ferromagnetic Ising model on the Cayley Tree

R. Mélin^{1, 2}

¹ Centre de Recherches sur les Très Basses Températures UPR 5001 CNRS, 25 avenue des Martyrs, BP 166X, 38042 Grenoble Cedex, France
² NEC Research Institute, 4 Independence Way, Princeton, NJ-08540, USA

(Received 20 May 1996, revised 11 July 1996, accepted 29 July 1996)

Abstract
We analyze the magnetization and the overlap distributions on the ferromagnetic Cayley tree. Two quantities are investigated: the asymptotic scaling of all the moments of the magnetization and overlap distributions, as well as the computation of the fractal dimension of the magnetization and overlap probability measures.