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

Abstract

The magnetic order-disorder layering transitions of a spin-1 Ising model are investigated, under the effect of a variable surface crystal field $Δ_{s}$, 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 $Δ_k=Δ_s/k^α$, $k=1,2,...,N$ and $α$ 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 $α$. On the other hand, the thermal behaviour of the surface magnetisation for a fixed value of the surface crystal field $Δ_{s}$ and selected values of the parameter $α$ are established.