Lahoussine Laanait

SOS approximants for Potts crystal shapes

Abstract An approximation made when replacing the orientation dependent Potts model surface tension by the SOS one is rigorously estimated. As a result, an SOS model may be used for an explicit and precise construction of crystal and meniscus shapes for Potts models at low temperatures.

Multilayer wetting in partially symmetricq-state models

When several phases coexist, the interface between two phases can be wetted by several films of the other phases. This is calledmultilayer wetting and can be characterized by the behavior of thespreading coefficients, which relate the surface tensions between the different phases. In this paper we consider a class of models which can exhibit a sequence of phase transitions. With some new correlation inequalities, we prove the positivity of a family of spreading coefficients. These inequalities, together with a thermodynamic argument, lead to the conclusion of multilayer wetting. These results generalize earlier results where single-layer interfacial wetting was obtained for the Potts model.

A lattice model for the line tension of a sessile drop

Within a semi-infinite three-dimensional lattice gas model describing the coexistence of two phases on a substrate, we study, by cluster expansion techniques, the free energy (line tension) associated with the contact line between the two phases and the substrate. We show that this line tension, is given at low temperature by a convergent series whose leading term is negative, and equals 0 at zero temperature.

Surface Transitions of the Semi-Infinite Potts Model I: The High Bulk Temperature Regime

We propose a rigorous approach of Semi-Infinite lattice systems illustrated with the study of surface transitions of the semi-infinite Potts model.

Memory capacity in neural networks with spatial correlations between attractors

We consider the neural network model (Miyashita, 1988. Griniasty et al., 1993) proposed to describe neurophysiological experiments in which structurally uncorrelated patterns are converted into spatially correlated attractors. For such a network of N neurons and for values of the coupling constant a between succeeding patterns, taken in the interval [0,12), we prove the existence of a threshold storage capacity αc(a) such that there exists a local minima (in the energy function) near each of the M(N)(

More results on the Ashkin-Teller model

We analyze the low-temperature phase diagram of the Ashkin-Teller model for real values of the quadratic and quartic coupling constants.

Phase diagrams of a lattice-gas model for micellar binary solutions

Using the mean-field approximation, we study the phase diagrams of the micellar binary solutions in the presence of a chemical potential of the amphiphiles (h) and the attraction interaction intermicellar parameter (J) for different values of competing interactions ( and ).

Absence of the partially ordered phase in theq-state models

We investigate theq-state models called (Nα,Nβ) model using an infinitesimal Migdal-Kadanoff renormalization-group method. We distinguish two cases namely the isotropic model and the anisotropic model. The first one presents a critical value ofq,qc such that forq<qc we obtain an Ashkin-Teller phase diagrams while forq>qc the partially ordered phase disappears then the model exhibits only phase transition between ferromagnetic phase and disordered one. The phase diagrams in the second case are qualitatively similar to one obtained forZ(6) model for all values ofq.

Phase diagrams of the semi-infiniteZ(q) models by real space renormalization-group method

We investigate the three-dimensional semi-infiniteZ(q) models using an infinitesimal Migdal-Kadanoff method. A rich variety of phase diagrams is obtained. The massless spin-wave phase which appears in the infinite two-dimensionalZ(q) models on the Clock line between the disordered and ferromagnetic phase forq≧qc is also present in the semi-infinite system on the surface when the bulk is disordered. We also observe that if the bulk is in the phase to which the symmetry is engendered by a subgroupZ(p), such thatp<q, the surface of the system is in the same phase or in a less symmetrical phase to which the symmetry is engendered by a subgroupZ(m) ofZ(p) such thatp=αm (m≦p) with α an integer number satisfying 1≦α≦p. The case α=p corresponds to the least symmetrical phase. Since the infiniteZ(q) models exhibit a rich variety of phase transitions and multicritical points, the semi-infinite models present new ordinary, extraordinary, surface and special phase transitions which do not occur in the semi-infinite Ising-like systems. As theZ(q) model transforms into theX−Y model whenq→∞, we have deduced the phase diagram of the semi-infiniteX−Y model. It is qualitatively similar to the phase diagram of the semi-infinite Ising model.