Study of the Ashkin Teller model with spins $S$ = $1$ and $\sigma$ = $3/2$ subjected to different crystal fields using the Monte-Carlo method

Using the Monte-Carlo method, we study the magnetic properties of the Ashkin-Teller model (ATM) under the effect of the crystal field with spins $S = 1$ and $\sigma = 3/2$. First, we determine the most stable phases in the phase diagrams at temperature $T = 0$ using exact calculations. For higher temperatures, we use the Monte-Carlo simulation. We have found rich phase diagrams with the ordered phases: a Baxter $3/2$ and a Baxter $1/2$ phases in addition to a $\left\langle \sigma S\right\rangle$ phase that does not show up either in ATM spin 1 or in ATM spin $3/2$ and, lastly, a $\left\langle \sigma\right\rangle = 1/2$ phase with first and second order transitions.