Phase diagram of the random field Ising model on the Bethe lattice.
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 regimes. 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 results obtained do not coincide with the lower bound for the onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If Bruinsma's estimate proves correct, this would hint at a region of coexistence of stable ferromagnetic phases and a stable paramagnetic phase.
Nowotny
Thomas
T
Institut für Theoretische Physik, Universität Leipzig, P. O. Box 920, 04109 Leipzig, Germany.
Patzlaff
Heiko
H
Behn
Ulrich
U