2001/06/30 by Thomas Nowotny, Heiko Patzlaff, Ulrich Behn · 1 citation
Mathematics · Physics and Astronomy · #Opinion Dynamics and Social Influence #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.016127
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
arxiv created 2001/09/24 · openalex publication_date 2001/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.