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Physica A Statistical Mechanics and its Applications

A general view on the critical behavior in the effective field theory approximation of the Ising model with arbitrary coordination number

E. Jurčišinová, Marian Jurčisin

Published Apr 8, 2019• 5 citations
Publisher
DOI
10.1016/j.physa.2019.04.117

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The system of two polynomial equations is derived for direct simultaneous determination of the critical temperatures of the spin-1 Ising model on lattices with arbitrary values of the coordination number in the single-site cluster effective field theory approximation. Analysis of the critical temperatures allows to determine simple linear function 2z/3−1/2 that approximates the critical temperatures of the model with very high precision for all values of the coordination number z. It is demonstrated that the system of two equations for the critical temperatures of the model can be reduced to the corresponding single equation in the cases with z=3,4, and 5. In addition, the system of entirely algebraic polynomial equations for the determination of the spontaneous magnetization of the model simultaneously for all values of the coordination number is also derived and discussed.
An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the multi-spin correlations systematically in a representative manner, as well as its single site counterparts in the system and gives results for the critical temperature of the system much better than those of the other works in the literature. The formulation can be easily applied to various extensions of s-1/2 Ising models, as long as the system contains only the nearest neighbor interactions as spin-spin interactions.
An improved unified formulation based on the effective field theory is introduced for a spin-1 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the multi-spin correlations systematically in a representative manner, as well as its single site counterparts in the system and gives much better results for critical temperature, in comparison with the other works in the literature. The formulation can be easily used to various kinds of spin-1 Ising models, as long as the system contains only the nearest neighbor interactions as spin-spin interactions.