In order to study the effect of the anisotropy parameter on the two coupled Ising models, we propose an Ashkin-Teller model (ATM) with spin variable S=1. Using an effective-field theory, we show that near the partially ordered phase ${\mathrm{PO}}_{1}$ that appears in spin-1/2 ATM, this model presents a new partially ordered phase ${\mathrm{PO}}_{2}$ . The anisotropy parameter introduces a first-order phase transition between different phases. However, the model exhibits a rich variety of phase diagrams and higher-order critical points.In order to study the effect of the anisotropy parameter on the two coupled Ising models, we propose an Ashkin-Teller model (ATM) with spin variable S=1. Using an effective-field theory, we show that near the partially ordered phase ${\mathrm{PO}}_{1}$ that appears in spin-1/2 ATM, this model presents a new partially ordered phase ${\mathrm{PO}}_{2}$. The anisotropy parameter introduces a first-order phase transition between different phases. However, the model exhibits a rich variety of phase diagrams and higher-order critical points.

Physical review. B, Condensed matterMay 1, 199711 citations

Numerical study of the spin-1 Ashkin-Teller model

M. Badehdah, Smain Bekhechi, A. Benyoussef +1 more

Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase ${\mathrm{PO}}_{2}$ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase ${\mathrm{PO}}_{2}$ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.

Physical review. B, Condensed matterMar 1, 199915 citations

{\mathrm{PO}}_{1}

that appears in spin-1/2 ATM, this model presents a new partially ordered phase

{\mathrm{PO}}_{2}

. The anisotropy parameter introduces a first-order phase transition between different phases. However, the model exhibits a rich variety of phase diagrams and higher-order critical points.

{\mathrm{PO}}_{2}

which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.