Phase diagrams of 2D Ashkin-Teller model within the effect of crystal field and quantum transverse field

In this work, we have analyzed the behavior of the 2D Ashkin-Teller model with spin-1 under the effect of the quantum transverse field and longitudinal crystal field. However, using mean field theory, three new diagrams of phase are found by varying the crystal field values. On the other hand, three others new phase diagrams with different quantum transverse field values. Therefore, multicritical behaviors are studied as a function of four-spin interaction coefficient(J4∕J1). Moreover, for the objective of assuring the existence of the different phases in the phase diagrams, we have plotted in addition the variation of the transverse field as a function of crystal field.