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

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 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

Crossover component in non critical dissipative sandpile models

The effect of bulk dissipation on non critical sandpile models is studied using both multifractal and finite size scaling analyses. We show numerically that the local limited (LL) model exhibits a crossover from multifractal to self-similar behavior as the control parameters $h_{ext}$ and $\epsilon$ turn towards their critical values, i.e. $h_{ext} \to 0^+$ and $\epsilon \to \epsilon_c$. The critical exponents are not universal and exhibit a continuous variation with $\epsilon$. On the other hand, the finite size effects for the local unlimited (LU), non local limited (NLL), and non local unlimited (NLU) models are well described by the multifractal analysis for all values of dissipation rate $\epsilon$. The space-time avalanche structure is studied in order to give a deeper understanding of the finite size effects and the origin of the crossover behavior. This result is confirmed by the calculation of the susceptibility.Comment: 13 pages, 10 figures, Published in European Physical Journal

Effect of disorder in magnetic and biological systems

Using replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes, and a generalization of Schneider and Pytte model to the l-component classical spin vector model are presented. In the first model, we study the effects of global fluctuations of the surface normal to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. In the second model, effects of a Gaussian random field on the phase transition of the l-component classical spin vector model are investigated. The phase diagrams are obtained in the cases l=1 and l=3, in opposite to what has been predicted by Schneided and Pytte. The results we obtain, for l=1 and l=3 show that the model exhibits a second-order, tricritical point and a first-order transition depending on the value of the =random field.Using replica formalism, a generalization of a recent mean field model corresponding to the observed wrinkling transition in randomly polymerized membranes, and a generalization of Schneider and Pytte model to the l-component classical spin vector model are presented. In the first model, we study the effects of global fluctuations of the surface normal to the flat membrane, which can be introduced by a random local field. In absence of these global fluctuations, we show that, the model exhibits both continuous and discontinuous transitions between flat and wrinkled phases, contrary to what has been predicted by Bensimon et al and Attal et al. Phase diagrams both in replica symmetry and in breaking of replica symmetry in sense of Almeida and Thouless are given. We have also investigated the effects of global fluctuations on the replica symmetry phase diagram. We show that, the wrinkled phase is favored and the flat phase is unstable. For large global fluctuations, the transition between wrinkled and flat phases becomes first order. In the second model, effects of a Gaussian random field on the phase transition of the l-component classical spin vector model are investigated. The phase diagrams are obtained in the cases l=1 and l=3, in opposite to what has been predicted by Schneided and Pytte. The results we obtain, for l=1 and l=3 show that the model exhibits a second-order, tricritical point and a first-order transition depending on the value of the =random field