Phase transitions in the anisotropic Ashkin–Teller model

By using mean-field approximation (MFA) and Monte-Carlo (MC) simulations, we have studied the effect of the anisotropy on the phase diagrams of the Ashkin–Teller model (A.T.M.) on a hypercubic lattice. By varying the strength of the anisotropic parameter, partially ordered phases, connected by symmetry, and denoted by σ and S appear in all dimensions d>1 as in the three dimensional isotropic case for antiferromagnetic interactions. The MC simulations reduce the varieties of phase diagrams obtained from MFA to one variety. In d=2 the phase diagrams present Ising-like phase transitions while in d=3 a first order phase transition and then multicritical points appear.