Abstract
A new type of effective-field theory that has recently been used with success for many applications concerning the two-state transverse Ising model (spin-12 TIM), is herein extended to the spin-1 TIM. The method, which can explicitly and systematically include correlation effects, is illustrated by employing its simplest approximation version, in which multispin correlations are neglected. The lines of critical points in the T-Ω plane as well as the thermal behavior of all relevant statistical-mechanical quantities are analysed for several lattice structures and compared with the standard mean-field predictions. It is shown that the present formalism, in spite of its simplicity, yields results quite superior to those currently obtained within the molecular-field approximation.
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