Thomas Nowotny, Heiko Patzlaff, Ulrich Behn
Published 2001-06-05, updated 2001-09-24Version 3
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.
Comments: Article has been condensed and reorganized; Figs 3,5,6 merged; Fig 4 omitted; Some discussion added at end of Sec. III; 9 pages, 5 figs, RevTeX4, AMSTeX
The Random Field Ising Model on Hierarchical Lattices I: Phase Diagram and Thermodynamics
Zero Temperature Hysteresis in Random Field Ising Model on Bethe Lattices: approach to mean field behavior with increasing coordination number z
The Fredrickson-Andersen model with random pinning on Bethe lattices and its MCT transitions
