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

Incommensurate nodes in the energy spectrum of weakly coupled antiferromagnetic Heisenberg ladders

Heisenberg ladders are investigated using the bond-mean-field theory [M.Azzouz, Phys. Rev. B 48, 6136 (1993)]. The zero inter-ladder coupling energy gap, the uniform spin susceptibility and the nuclear magnetic resonance spin-relaxation rate are calculated as a function of temperature and magnetic field. For weakly coupled ladders, the energy spectrum vanishes at incommensurate wavevectors giving rise to nodes. As a consequence, the spin susceptibility becomes linear at low temperature. Our results for the single ladder successfully compare to experiments on SrCu_2O_3 and (VO)_2P_2O_7 materials and new predictions concerning the coupling to the magnetic field are made.Comment: 4 revtex pages, 3 figures available upon reques

Interface disorder and layer transitions in Ising thin films

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 forma

Surface reentrance in the semi-infinite spin-1 Ising models

The critical behavior of the semi-infinite Blume-Capel and Blume-Emery-Griffiths models is investigated in the pair approximation of the Cluster Variation Method. Equations for bulk and surface order parameters and n.n. correlation functions are given, from which analytical expressions for the second order bulk and surface critical temperatures are derived. The phase diagrams of the Blume-Capel model are classified, and the existence of a surface first order transition is discussed. This transition is shown to be, under certain conditions, slightly reentrant, and the behavior of the surface order parameters and correlation functions is given for such a case. The extension of our results to the Blume-Emery-Griffiths model is briefly discussed.Comment: 17 pages, 14 figures (PostScript, appended), POLFIS-TH.19/9

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