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Phase diagram of the random field Ising model on the Bethe lattice

Thomas Nowotny·Heiko Patzlaff·Ulrich Behn
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Abstract

The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the ferromagnetic and paramagnetic regime. Refining arguments of Bleher, Ruiz and Zagrebnov [J. Stat. Phys. 93, 33 (1998)] an exact upper bound for the existence of a unique paramagnetic phase is found which considerably improves the earlier results. Several numerical estimates of transition lines between a ferromagnetic and a paramagnetic regime are presented. The obtained results do not coincide with a lower bound for the onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If the latter one proves correct this would hint to a region of coexistence of stable ferromagnetic phases and a stable paramagnetic phase.

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Thomas Nowotny, Heiko Patzlaff, Ulrich Behn. 2001-09-24. Phase diagram of the random field Ising model on the Bethe lattice. https://doi.org/10.1103/physreve.65.016127

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