arXiv subjects
Publications and source records attributed to Salvador Miracle-Sole.
The shape of an equilibrium crystal is obtained, according to the Gibbs thermodynamic principle, by minimizing the total surface free energy associated to the crystal-medium interface. To study the solution to this problem, known as the Wulff construction, is the object of the article.
Mathematical aspects of the theory of interfaces in statistical mechanics are discussed.
Two theorems on the theory of cluster expansions for an abstract polymer system are reported.
We present some illustrations for the claim that already by looking at the ground states of classical lattice models, one may meet some interesting and non-trivial structures.
According to the Wulff construction the shape of the equilibrium crystal is determined by the surface tension considered as a function of the interface orientation. We present some (conjectured) approximate solutions and some rigorous results concerning this function, in the case of a lattice gas, and apply them to study the shape of the equilibrium crystal and, in particular, the shape of the facets of this crystal.
The statistical mechanics of SOS (solid-on-solid) 1-dimensional models under the global constraint of having a specified area between the interface and the horizontal axis, is studied. We prove the existence of the thermodynamic limits and the equivalence of the corresponding statistical mechanics. This gives a simple alternative microscopic proof of the validity of the Wulff construction for such models.
Several aspects of the theory of the coexistence of phases and equilibrium forms are discussed. In section 1, the problem is studied from the point of view of thermodynamics. In section 2, the statistical mechanical theory is introduced. We consider, in particular, the description of the microscopic interface at low temperatures and the existence of a free energy per unit area (surface tension). In section 3, a proof is given of the microscopic validity of the Wulff construction in a simplified model of a two-dimensional interface. Finally, in section 4, the roughening transition and the formation of facets in an equilibrium crystal are studied. Appendices A and B concern, respectively, the first and second points of section 2, mentioned above.
A short exposition with complete proofs of the theory of cluster expansions for an abstract polymer system is presented.
We study the solid-on-solid interface model above a horizontal wall in three dimensional space, with an attractive interaction when the interface is in contact with the wall, at low temperatures. The system presents a sequence of layering transitions, whose levels increase with the temperature, before the complete wetting above a certain value of this quantity.
Within a lattice model describing a binary mixture with fixed concentrations of the species we discuss the relation-ship between the surface tension of the mixture and the concentrations.
We consider the problem of the Winterbottom's construction and Young's equation in the presence of a rough substate and establish their microscopic validity within a 1+1-dimensional SOS type model. We then present the low temperature expansion of the wall tension leading to the Wenzel's law for the wall tension and its corrections. Finally, for a fix roughness, we compare the influence of different geometries of the substrate on wetting properties. We show that there is an optimal geometry with a given roughness for a certain class of simple substrates. Our results are in agreement and explain recent numerical simulations.