The Curie Temperature of the Two-Dimensional Quadratic Ising Ferromagnet with Mixed Spins of S=1⁄2 and S=1

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For the two-dimensional quadratic Ising ferromagnet with mixed spins of S=1⁄2 and S=1, the Curie temperature T_c has been calculated with the use of Bethe-Peierls theory. Assuming the bilinear exchange interactions J₁ between nearest neighbors (n.n.) of the different spins, J₂ and J₃ between two kinds of next nearest neighbors (n.n.n.) of the same spins, and the biquadratic exchange J₁′ between n.n. and J₂′ between n.n.n. of spins S=1, the behaviors of T_c as a function of these exchange parameters are investigated. The ferromagnetic order is shown to be unstable when the ratio J₁′⁄J₁ amounts to −1.85. It is also pointed out that J₁′ and J₂′ give a qualitatively different effect on T_c. Furthermore, it turns out that the exchange interaction J₂ between n.n.n. of spins S=1 gives more significant effect on T_c than J₃ between n.n.n. of spins S=1⁄2.