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

TL;DR

This study explores the phase behavior of the Ashkin-Teller model with mixed spins $S=1$ and $\sigma=3/2$ under crystal fields, using Monte Carlo simulations to map phase diagrams and identify novel phases.

Contribution

It introduces a detailed Monte Carlo analysis of the Ashkin-Teller model with mixed spins, revealing new phases not seen in single-spin models.

Findings

Identified multiple ordered phases including Baxter $3/2$, Baxter $1/2$, and a unique $\sigma S$ phase.

Discovered phase transitions of both first and second order.

Mapped complex phase diagrams at finite temperatures.

Abstract

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.