Improved product average decomposition method for the Ising ferromagnet with two- and four-spin interaction
O Mitran; O Mitran; Phys. Dept., Concordia Univ., Montreal, Que., Canada
Журнал:
Journal of Physics C: Solid State Physics
Дата:
1979-11-28
Аннотация:
Two improvements to a previous calculation of the transition temperature for the three-dimensional Ising ferromagnet with combined two- and four-spin interaction are presented. The first improvement follows from the complete implementation of a refined product average decomposition (PAD) method which distinguishes between nearest-neighbour and non-nearest-neighbour pairs. The second improvement comes from a comparison of the value for the ordinary two-spin interaction average of order four calculated using the PAD method, with its more accurate value calculated using a critical correlation-function approximation method. The comparison with the available values of the transition temperature for the FCC lattice obtained from low-temperature expansions shows that the errors are below 0.1% at alpha = infinity ( alpha =J<sub>4</sub>/J<sub>2</sub>), below 5.8% for alpha <or=2, and below 2.4% for alpha <or=1. At alpha =0 the errors are less than 0.3%. For intermediate values of alpha (4<or= alpha <or=8, for example) the errors are about 11%.
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