Abstract
The very recently improved treatment proposed by Tucker on the Honmura-Kaneyoshi exponential operator technique is herein extended to treat the anisotropic Blume-Emery-Griffiths model. It is shown that this procedure leads to an exact set of mutually coupled equations which can explicitly and systematically include effects of correlations. The method is illustrated in a honeycomb lattice by employing its simplest approximate version, in which multispin correlations are neglected. Within this framework the authors find that the transition temperature is double valued under certain conditions of competing bilinear and biquadratic interactions, suggesting the occurrence of re-entrant behaviour in both first- and second-order phase boundary lines.
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