Study of Blume–Emery–Griffiths model by a modified Bethe-Peierls method

Abstract

We present here a study of the Blume–Emery–Griffiths (BEG) model for general spins using a modified Bethe–Peierls (BP) method calling it the Bethe–Peierls–Lines (BPL) method, incorporating the well known Lines approximation. We compare our results of BPL as well as BP methods for the ferro-to para-magnetic transition temperatures Tc with those available from other theories such as the Correlated-Effective-Field Theory (CEFT), Cluster Variation Method (CVM) and the Monte-Carlo (MC) method. We find that our BPL method gives results for variation of Tc with the single-ion uniaxial anisotropy (D) and biquadratic interaction (J') coefficients close to those obtained by CVM method for spin S = 1 on a honeycomb lattice. We also find that the BPL results are in good agreement for the cubic lattice for S = 3/2 and J' = 0 with those of the MC results, and for S = 1 and J' = −0.5J with those of the CVM results. For these three dimensional lattices our BPL method gives the correct reentrant behaviour for negative values of J'. We also compare our BP and BPL results for magnetic susceptibility with those of the CEFT for S = 3/2 and 3 nearest neighbours and find fairly good agreement for D > 0.