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

The magnetic order-disorder layering transitions of a spin-1 Ising model are investigated, under the effect of a variable surface crystal field AS, 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. (C) 2002 Elsevier Science B.V. All rights reserved.