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

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

2001-06-05

arxiv.org/abs/cond-mat/0106074v3

Physics

Condensed Matter

Disordered Systems and Neural Networks

Article has been condensed and reorganized; Figs 3,5,6 merged; Fig 4 omitted; Some discussion added at end of Sec. III; 9 page

Scientific paper

10.1103/PhysRevE.65.016127

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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