Critical properties of the spin-1 Ashkin-Teller model from the differential operator method

Abstract

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.