We have investigated numerically a statistical model of four component systems, which exhibit two critical temperatures, called the Ashkin-Teller model (ATM). The effects of, the anisotropy coupling, the single ion potential field and the mixed spin on the structure of the phase diagram have been studied. The model presents a rich variety of phase transitions which meet on tricritical or multicritical points. Different partially ordered phases with a partially broken symmetry appears at high temperatures. Their region of stability and their structure depend on the phase parameter space. The nature of critical lines which bound these partially ordered phases depends on the coupling parameters and the crystalline anisotropy.