Order-disorder layering transitions of a spin-1 Ising model in a variable crystal field

TL;DR

This study investigates the magnetic order-disorder layering transitions in a spin-1 Ising model with a variable surface crystal field, revealing phase diagrams, tricritical points, and reentrant phenomena dependent on film thickness and crystal field distribution.

Contribution

It introduces a model with a variable surface crystal field affecting layering transitions, including phase diagrams and critical phenomena, using mean field theory.

Findings

Identified phase diagrams with tricritical points.

Discovered reentrant phenomena in the first layers.

Showed dependence of critical points on film thickness and distribution exponent.

Abstract

The magnetic order-disorder layering transitions of a spin-1 Ising model are investigated, under the effect of a variable surface crystal field $\Delta_{s}$, using the mean field theory. Each layer $k$, of the film formed with $N$ layers, disorders at a finite surface crystal field distributed according to the law $\Delta_k=\Delta_s/k^\alpha$, $k=1,2,...,N$ and $\alpha$ being a positive constant. We have established the temperature-crystal field phase diagrams and found a constant tricritical point and a reentrant phenomenon for the first $k_0$ layers. This reentrant phenomenon is absent for the remaining $N-k_0 $ layers, but the tricritical points subsist and depend not only on the film thickness but also on the exponent $\alpha$. On the other hand, the thermal behaviour of the surface magnetisation for a fixed value of the surface crystal field $\Delta_{s}$ and selected values of the parameter $\alpha$ are established.