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We study the magnetic properties of a mixed Ising ferrimagnetic system, in which the two interacting sublattices have spins $\sigma$, $(\pm 1/2)$ and spins $S$, $(\pm 3/2,\pm 1/2)$ in the presence of a random crystal field, with the mean field approach. The obtained results show the existence of some interesting phenomena, such as the appearance of a new ferrimagnetic phase namely the partly ferrimagnetic phase $(m_{\sigma}=\frac{-1}{2},m_S=+1)$ and consequently the existence of three topologically different types of phase diagrams. The effect of increasing the exchange interaction parameter $J$, at very low temperature is investigated. The transitions shown in these phase diagrams are in good agreement with those obtained in the ground state case.

We study the spin-1 Ising model with bilinear and biquadratic exchange interactions and single-ion crystal field. In addition to the four usual phases: disordered DIS, ferromagnetic FER, antiquadrupolar AQU and ferrimagnetic FRI, we found three new phases in the case of a thin magnetic film, namely: the sublattice A non magnetic phase NMA, the sublattice B non magnetic phase NMB and the global non magnetic phase NMG. These phases are studied, for each layer of the film, either in the temperature-crystal field plane $(T,\Delta)$ or in the biquadratic coupling-crystal field plane $(d,\Delta)$, for diferent film thicknesses. On the other hand, the thermal behaviour of the layer quadrupolar moments $q_{A}, q_{B}$ and layer magnetisations $m_{A}, m_{B}$ are investigated for negative values of the biquadratic coupling and crystal field. It is also found that for fixed values of the biquadratic coupling, the temperature and the crystal field, each layer of the film can belong to a differnt phase. To illustrate this situation, an example is given for $d=-3.0$, $\Delta =-3.0$ and $T=1.3$., Comment: 8 pages 15 figures

Wetting phenomena plays an interesting role in the technological development of materials. Recently, much attention has been directed to the study of magnetic solid films. To understand, theoretically, the effect of surface on wetting and layering transitions in these systems, we will give in this chapter a presentation of several relevant recent theoretical works realized on wetting and layering transitions in which we explain how the nature of surface can affect the behavior of wetting and layering transitions. Using different spin systems models and different numerical and approximate methods such as mean field and effective field theories, real space renormalization group technique, transfer matrix method and Monte-Carlo simulations, it is found that the wetting and layering transitions depend on the nature of the surface magnetic field, the surface coupling strength, the surface crystal field, the geometry of surface, the in-homogeneity of substrate and the quantum fluctuations at the surface�

The disorder and layer transitions in the interface between an Ising spin-1/2 film denoted $(n)$, and an Ising spin-1 film denoted $(m)$, are studied using Monte Carlo simulations. The effects of both an external magnetic field, acting only on the spin-1/2 film, and a crystal magnetic field acting only on the spin-1 film, are studied for a fixed temperature and selected values of the coupling constant $J_p$ between the two films. It is found that for large values of the constant $J_p$, the layers of the film $(n)$, as well as those of the film $(m)$, undergo a first order layering transition. On the other hand, the only disordered layer of the film $(n)$ is that one belonging to the interface films $(n)/(m)$, for any values of the crystal field $\Delta$. We show the existence of a critical value of the crystal field $\Delta_c$, above which this particular layer of the film $(n)$ is disordered. We found that $\Delta_c$ depends on the values of the constant coupling $(J_p)$ between the two films., Comment: 6 pages Latex, 13 figures Postscript format

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 postscript

We study the surface substrate inhomogeneity effect on the wetting of a spin-1/2 Ising ferromagnetic film in an external magnetic field $H$, using Monte Carlo simulations. It is found the inhomogeneity leads to the formation of islands of positive spins in each layer. However, depending on the values of $H$, for a fixed surface magnetic field $H_s$, each layer exhibits three different phases; totally wet, nonwet and partially wet (PW). In the latter case, we show the existence of three distinct configurations namely: A configuration (PWTD) in which the layer is partially wet with a total disconnection between islands; (PWPD) a configuration in which the layer is partially wet with a partial disconnection between islands; (PWTC) a configuration in which the layer is partially wet and the islands are totally connected. Furthermore, we show that an increase of $H_s$ values breaks the bonds connecting some islands of the phase (PWTC) which leads to an expansion of the (PWPD) region. On the other hand, the frequency distribution and the mean size of island are investigated in the (PWTD) region for fixed values of temperature $T$, $H_s$ and $H$. Moreover, we show the existence of 3D-islands resulting from the formation of islands in each layer.

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 format