Phase Diagram for Ashkin–Teller Model on Bethe Lattice

Abstract

Using the recursion method, we study the phase transitions of theAshkin–Teller model on the Bethe lattice, restricting ourselves to the caseof ferromagnetic interactions. The isotropic Ashkin–Teller model and theanisotropic one are respectively investigated, and exact expressions for thefree energy and the magnetization are obtained. It can be found that each ofthe three varieties of phase diagrams, for the anisotropic Ashkin–Tellermodel, consists of four phases, i.e., the fully disordered paramagneticphase Para, the fully ordered ferromagnetic phase Ferro, and twopartially ordered ferromagnetic phases ⟨σ⟩and ⟨σs⟩, while the phase diagram, for theisotropic Ashkin–Teller model, contains three phases, i.e., the fullydisordered paramagnetic phase Para, the fully ordered ferromagnetic phase Baxter Phase, and the partially ordered ferromagnetic phase ⟨σs⟩.