Monte Carlo Study of Order-Disorder Layering Transitions in the Blume-Capel Model

The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first $k_0$ layers from the surface, where $k_0$ is exactly the number of layering transitions allowed by the ground state study. The layer magnetizations $m_k$, the magnetic susceptibilities $\chi_{m,k}$ and the quadrupolar magnetic susceptibilities $\chi_{q,k}$ and the corresponding critical exponent, for each layer $k$, are also investigated.Comment: 10 pages Latex, 9 figures Postscript forma

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 $\Delta_{s}$, 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.Comment: 10 Pages Latex, 9 Figures Postscript. To appear in JMMM (2002

A Monte Carlo study of random surface field effect on layering transitions

The effect of a random surface field, within the bimodal distribution, on the layering transitions in a spin-1/2 Ising thin film is investigated, using Monte Carlo simulations. It is found that the layering transitions depend strongly on the concentration $p$ of the disorder of the surface magnetic field, for a fixed temperature, surface and external magnetic fields. Indeed, the critical concentration $p_c(k)$ at which the magnetisation of each layer $k$ changes the sign discontinuously, decreases for increasing the applied surface magnetic field, for fixed values of the temperature $T$ and the external magnetic field $H$. Moreover, the behaviour of the layer magnetisations as well as the distribution of positive and negative spins in each layer, are also established for specific values of $H_s$, $H$, $p$ and the temperature $T$. \\Comment: 5 pages latex, 6 figures postscrip

Edge wetting of an Ising three-dimensional system

The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field (MF) theory and Monte Carlo (MC) simulations. For T=0, the ground state phase diagram shows that there exist only three allowed transitions, namely: surface and bulk transition, surface transition and bulk transition. However, there exist a surface intra-layering temperature $T_{L}^{s}$, above which the surface and the intra-layering surface transitions occur. While the bulk layering and intra-layering transitions appear above an other finite temperature $T_{L}^{b} (\ge T_{L}^{s})$. These surface and bulk intra-layering transitions are not seen in the perfect surfaces case. Numerical values of $T_{L}^{s}$ and $T_{L}^{b}$, computed by Monte Carlo method are found to be smaller than those obtained using mean field theory. However, the results predicted by the two methods become similar, and are exactly those given by the ground state phase diagram, for very low temperatures. On the other hand, the behavior of the local magnetizations as a function of the external magnetic field, shows that the transitions are of the first order type. $T_{L}^{s}$ and $T_{L}^{b}$ decrease when increasing the system size and/or the surface magnetic field. In particular, $T_{L}^{b}$ reaches the wetting temperature $T_{w}$ for sufficiently large system sizes.Comment: 11 Pages latex, 12 Figures P

A Monte Carlo Study of the Order-Disorder Layering Transitions in the Blume-Capel Model

The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions allowed by the ground state study. For each layer 'k', the layer magnetisations mk , the magnetic susceptibilities χm,k and the quarupolar magnetic susceptibilities χq,k are also investigated.The order-disorder layering transitions, of the Blume-Capel model, are studied using the Monte Carlo (MC) simulations, in the presence of a variable crystal field. For a very low temperature, the results are in good agreement with the ground state study. The first order transition line, found for low temperatures, is connected to the second order transition line, seen for higher temperatures, by a tri-critical point, for each layer. The reentrant phenomena, caused by a competition of thermal fluctuations and an inductor magnetic field created by the deeper layers, is found for the first k0 layers from the surface, where k0 is exactly the number of layering transitions allowed by the ground state study. For each layer 'k', the layer magnetisations mk , the magnetic susceptibilities χm,k and the quarupolar magnetic susceptibilities χq,k are also investigated

Wetting of an Ising system with perfect and corrugated surfaces in a transverse field

Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of both the temperature and the transverse field on the wetting and layering transitions are established.Using the mean field theory, a comparative study of the wetting and layering transitions of a spin-1/2 Ising model with perfect and corrugated surfaces, is established. The phase diagrams are investigated and compared in the presence of both a longitudinal and surface fields. The effect of both the temperature and the transverse field on the wetting and layering transitions are established